Archive

Abstract:

The research aims to understand the design parameters of steam ejector nozzle on the performance of flash evaporation induced by the effect of a steam jet passing through it. The research concentrates on studying the effect of ejector nozzle outlet diameter on induced flow from preheated water in a specified evaporator using a subsonic ejector. The thermal energy extracted from the condensed steam mixture in the condenser is used to heat the water in the evaporator. The experimental tests investigate the effect of nozzle geometry on the induced evaporation process by changing nozzle outlet diameter while keeping the pressure of evaporator, condenser and primary steam constant. The experimental results proved that both primary and secondary steam mass flow rates increase versus nozzle outlet diameter, while the entrainment ratio of secondary to primary steam flow rates decreases due to the restricted increase of the secondary steam mass flow rate. The mathematical model prepared to simulate the behaviour of the subsonic ejector is validated using the comparison between experimental and theoretical results. The mathematical model showed that maximum entrainment of 0.57 is obtained at a primary steam pressure of 2 bars when the nozzle outlet diameter is fixed at 1.5 mm, while minimum entrainment ratio of 0.17 is estimated at 1.5 bar pressure related to primary steam when the nozzle outlet diameter is fixed at 2.5mm. The authors recommend defining nozzle geometrical parameters according to the operating conditions of the experimental test rig to enhance ejector efficiency.

Keywords:

Flash evaporation,Induced flow,Nozzle,Subsonic,Ejector,

Refference:

I. A. Ezzat et al., Investigation of steam jet flash evaporation with solar thermal collectors in water desalination systems, Thermal science and engineering progress, 20 (2020) 100720.
II. Antonio, et al., Thermodynamic modeling of an ejector with compressible flow by one dimensional approach, Entropy 14 (4) (2012) 599–614.
III. kavous Ariafar . Effect of Nozzle Geometry on a Model Thermo compressor Performance – a Numerical Evaluation. Journal ISME 2012
IV. Lam Ratna Raju, Ch. Pavan Satyanarayana, Neelamsetty Vijaya Kavya, : AN APPROACH FOR OPTIMISING THE FLOW RATE CONDITIONS OF A DIVERGENT NOZZLE UNDER DIFFERENT ANGULAR CONDITIONS, J. Mech. Cont.& Math. Sci., Vol.-15, No.-7, July (2020) pp 608-625.
V. M. Dennis. Solar Cooling Using Variable Geometry Ejectors, 2009, Croll Reynold Steam Ejectors, 2018, https://croll.com/vacuum-systems/applications/
VI. Mehran Ahmadi , Poovanna Thimmaiah ,Majid Bahrami ,Khaled Sedraoui, Hani H. Sait and Ned Djilali . Experimental and numerical investigation of a solar eductorassisted low-pressure water desalination system. Journal Science Bulletin 2016.
VII. N.M.K. Sarath Kumar, A. Vamsi Krishna, G. Shyam Mahesh, K. Bharath Kumar, M. Venkataiah, : CFD ANALYSIS OF RB211 AND CFM56 CHEVRON NOZZLES, J. Mech. Cont.& Math. Sci., Vol.-15, No.-7, July (2020) pp 405-415.

VIII. Natthawut Ruangtrakoon, Tongchana Thongtip, Satha Aphornratana, Thanarath Sriveerakul.CFD simulation on the effect of primary nozzle geometries for a steam ejector in refrigeration cycle. International Journal of Thermal Sciences 2012.
IX. R. Kelso, Applied aerodynamics: compressible flow, PowerPoint Presentation (2018).
X. Seyedali Sabzpoushan, Masoud Darband I and Gerry E. Schneider. Numerical Investigation on the Effects of Operating Conditions on the Performance of a Steam Jet-Ejector. Journal international Conference of Fluid Flow.
XI. S. Han, et al., One-dimensional numerical study of compressible flow ejector, AIAA
XII. J. 40 (7) (2002) 1469–1473.
XIII. S. Liu, et al., Thermodynamic analysis of steam ejector refrigeration cycle, Int. Refrigeration Air Conditioning Conf. (2014) 2306–2307.
XIV. Szabolcs Varga, Armando C. Oliveira, Xiaoli Ma and Siddig A. Omer. Comparison of CFD and experimental performance results of a variable area ratio steam ejector. International Journal of Low-Carbon Technologies • June 2011
XV. Szabolcs Vargaa, Armando C. Oliveiraa and Bogdan Diaconua. Numerical assessment of steam ejector efficiencies using CFD. International journal of refrigeration, 2009.
XVI. Vineet V. Chandra and M.R. Ahmed. Experimental and computational studies on a steam jet refrigeration system with constant area and variable area ejectors. Journal of Elsevier, 2013.

MODIFIED QUADRATURE ITERATED METHODS OF BOOLE RULE AND WEDDLE RULE FOR SOLVING NON-LINEAR EQUATIONS

Authors:

Umair Khalid Qureshi, Sanaullah Jamali, Zubair Ahmed Kalhoro, Abdul Ghafoor Shaikh

DOI NO:

https://doi.org/10.26782/jmcms.2021.02.00008

Abstract:

This article is presented a modified quadrature iterated methods of Boole rule and Weddle rule for solving non-linear equations which arise in applied sciences and engineering. The proposed methods are converged quadratically and the idea of developed research comes from Boole rule and Weddle rule. Few examples are demonstrated to justify the proposed method as the assessment of the newton raphson method, steffensen method, trapezoidal method, and quadrature method. Numerical results and graphical representations of modified quadrature iterated methods are examined with C++ and EXCEL. The observation from numerical results that the proposed modified quadrature iterated methods are performance good and well executed as the comparison of existing methods for solving non-linear equations.

Keywords:

Boole Rule and Weddle Rule,convergence criteria,existing methods,graph,results,

Refference:

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III. Liu, Z. and H. Zhang, Steffensen-Type Method of super third-order convergence for solving nonlinear equations, Journal of Applied Mathematics and Physics, vol 2, 581-586, 2014.
IV. Memon Kashif, Muhammad Mujtaba Shaikh, Muhammad Saleem Chandio, Abdul Wasim Shaikh, : A NEW AND EFFICIENT SIMPSON’S 1/3-TYPE QUADRATURE RULE FOR RIEMANN-STIELTJES INTEGRAL, J. Mech. Cont. & Math. Sci., Vol.-15, No.-11, November (2020) pp 132-148
V. Perhiyar, M. A., S. F. Shah and A. A. Shaikh, Modified Trapezoidal Rule Based Different Averages for Numerical Integration, Mathematical Theory and Modeling, Vol.9, No.9, 2019.
VI. Qureshi, U. K., A New Accelerated Third-Order Two-Step Iterative Method for Solving Nonlinear Equations, Mathematical Theory and Modeling, Vol: 8(5), 2018.
VII. Qureshi, U. K., I. A. Bozdar, A. Pirzada and M. B. Arain, Quadrature Rule Based Iterative Method for the Solution of Non-Linear Equations, Proceedings of the Pakistan Academy of Sciences, Pakistan Academy of Sciences A. Physical and Computational Sciences, vol: 56 (1): 39–43, 2019.
VIII. Qureshi, U. K., Z. A. Kalhoro, A. A. Shaikh and A. R. Nagraj, Trapezoidal Second Order Iterated Method for Solving Nonlinear Problems, University of Sindh Journal of Information and Communication Technology (USJICT), Vol: 2(2), 2018.
IX. Shaikh, M. M., M. S. Chandio and A. S. Soomro, A Modified Four-point Closed Mid-point Derivative Based Quadrature Rule for Numerical Integration, Sindh University Research Journal, SURJ (Science Series), 48(2), 2016.
X. Umar Sehrish , Muhammad Mujtaba Shaikh , Abdul Wasim Shaikh, : A NEW QUADRATURE-BASED ITERATIVE METHOD FOR SCALAR NONLINEAR EQUATIONS, J. Mech. Cont.& Math. Sci., Vol.-15, No.-10, October (2020) pp 79-93.
XI. Weerakoon, S. and T. G. I. Fernando, 2000, A Variant of Newton’ s Method with Accelerated Third-Order Convergence, Applied Mathematics Letters, vol 13 87-93.
XII. Zafar, F., Saira S. and C. O. E. Burg, New Derivative Based Open Newton-Cotes Quadrature Rules, Hindawi Publishing Corporation Abstract and Applied Analysis Volume 2014.
XIII. Zhao, W. and L. Hongxing, Midpoint Derivative-Based Closed Newton-Cotes Quadrature, Hindawi Publishing Corporation Abstract and Applied Analysis Volume 2013.

COMPARATIVE STUDY OF DIFFERENT SOLAR PHOTOVOLTAIC ARRAYS CONFIGURATION TO MITIGATE NEGATIVE IMPACT OF PARTIAL SHADING CONDITIONS

Authors:

D. P. Kothari, Anshumaan Pathak, Utkarsh Pandey

DOI NO:

https://doi.org/10.26782/jmcms.2021.02.00009

Abstract:

Growth of photovoltaic systems that require more and more productive alternatives, not only in micro-fabrication techniques but also in methods of energy extraction. In recent years, a large number of Maximum Power Point Tracking algorithms with various complexities over decades the ability to efficiently locate the global maximum under partial shading was followed by evolved. Partial Shading Conditions (PSC) play a major role in determining the energy and power productivity of a solar photovoltaic (SPV) system. Under PSC, the SPV panels receive varying levels of solar irradiance, resulting in a decrease in the power generation of the SPV system, and these losses in SPV panels can be minimized by adjusting the configuration of the array/module panels. The panels can be designed to increase production energy and power quality in several different configurations, such as Series(S), Parallel (P), Series-Parallel (SP), Complete Cross Tied (TCT), Bridge Linked (BL) and Honeycomb (HC). This work is aimed at presenting all the configurations already presented in the literature and referencing and evaluating the findings of PSC on SPV systems. In this paper, there are four 4-4 array configurations of solar photovoltaic panels to be addressed. Parallel series (SP), complete cross-linked (TCT), the bridge linked (BL) and honeycomb are four configurations (HC). To decide on the effect of shadow with 10 shading patterns, four simulated models were carried out. For the above-mentioned configuration, the simulated results indicate a power against voltage (PV) curve of 4 to 4 SPV array under PSC. This thesis will be a reference point for useful and important knowledge for researchers in the field of solar panels.

Keywords:

Photo-voltaic cells,Power Enhancement,Partial Shading,series-parallel (SP),total cross-tied (TCT),total cross-tied (TCT),honeycomb (HC),

Refference:

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XII. Markvart T 2016 From steam engine to solar cells: can thermodynamics guide the development of future generations of photovoltaics? WIREs Energy and Environment doi: 10.1002/wene.204
XIII. Amit Kumar, Rupendra Kumar Pachauri, Yogesh K. Chauhan Experimental Analysis of Proposed SP-TCT, TCT- BL and CT-HC Configurations under Partial shading Conditions
XIV. Seyedmahmoudian M Mekhilef S Rahmani R Yusof R and Shojaei A A 2014 Maximum power point tracking of partial shaded photovoltaic array using an evolutionary algorithm: A particle swarm optimization technique. J. of Renewable and Sustainable Energy 6(2) doi: 10.1063/1.4868025
XV. Pavlovic T and Ban Z 2013 An improvement of incremental conductance MPPT algorithm for PV systems based on the Nelder–Mead optimization. IEEE 6
XVI. Patel Hiren and Vivek Agarwal, “MATLAB-based modelling to study the effects of partial shading on PV array characteristics,” IEEE Transactions on Energy Conversion, vol. 23, no. 1 , pp. 302-310, 2008.
XVII. R. Ramaprabha and B. L. Mathur, “A comprehensive review and analysis of solar photovoltaic array configurations under partial shaded conditions,” International Journal of Photo energy, vol. 2012, 2012.
XVIII. Wang Yaw-Juen and Po-Chun Hsu, “An investigation on partial shading of PV modules with different connection configurations of PV cells,” Energy, vol. 36.5, pp. 3069-3078, 2011.
XIX. Wilson K. Rahul, Y. Srinivasa Rao, : EFFECTS OF PARTIAL SHADING ON DIFFERENT STRUCTURES OF SOLAR PHOTOVOLTAIC ARRAYS, J. Mech. Cont.& Math. Sci., Vol.-14, No.-6 November-December (2019) pp 845-854

NUMERICAL SIMULATION AND PERFORMANCE EVALUATION OF BEAM COLUMN JOINTS CONTAINING FRP BARS AND WIRE MESH ARRANGEMENTS

Authors:

Faisal Hayat Khan, M. Fiaz Tahir, Qaiser uz Zaman Khan

DOI NO:

https://doi.org/10.26782/jmcms.2021.02.00010

Abstract:

This research paper aims at a detailed study of the seismic performance of reinforced concrete Beam-Column Joint (BCJ) under quasi-static cyclic loading. Firstly, the numerical simulations of the previously experimented specimen have been performed by Finite Element Method (FEM) using ABAQUS 6.14. Secondly, the parametric study has been conducted for the validated model by the introduction of Fiber Reinforced Polymer (FRP) bars in the form of Carbon Fiber Reinforced Polymer (CFRP) and Glass Fiber Reinforced Polymer (GFRP). An investigation has also been carried out to study the effect of T-304 Stainless Steel Wire Mesh (SSWM) on the strengthening of the finite element numerical model. Ten different numerical models were evaluated which included two sets, the first set includes five models having a control model and the models in which the steel reinforcement was partially or full replaced by CFRP and GFRP bars, the next set contains further five models in which stainless-steel wire mesh was wrapped around the core concrete in the aforementioned models. The results show the evidence for GFRP bars to be used in seismic designing, as have shown an almost 100% increase in deflection with the requisite amount of energy dissipation and ultimate strength capacities. Furthermore, the crack initiation was delayed by 30-40% in terms of deflection when stainless-steel wire mesh was used which controls the damage in the critical zone of BCJ. The prime factors in controlling the crack pattern, energy dissipation, ultimate strength and deflection capacity of beam-column joint were the position of FRP bars, reinforcement ratio, dimensions of beam-column joints and the available economy.

Keywords:

CFRP bars,GFRP bars,wire mesh,beam-column joint,

Refference:

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XI. Karabinis, T. C. Rousakis & G. E. Manolitsi (2008) 3D Finite-Element Analysis of Substandard RC Columns Strengthened by Fiber-Reinforced Polymer Sheets. Journal of Composites for Construction, 12, 531-540.
XII. Kazemi, J. Li, S. Lahouti Harehdasht, N. Yousefieh, S. Jahandari & M. Saberian (2020) Non-linear behaviour of concrete beams reinforced with GFRP and CFRP bars grouted in sleeves. Structures, 23, 87-102.
XIII. Kmiecik & M. Kami´nski (2011) Modelling of reinforced concrete structures and composite structures with concrete strength degradation taken into consideration. Archives of Civil and Mechanical Engineering, vol. 11, pp. 623–636.
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XVI. M. Fiaz Tahir (2015) Response of Seismically Detailed Beam Column Joints Repaired with CFRP Under Cyclic Loading. Arabian Journal for Science and Engineering, 41, 1355-1362.
XVII. Manaha, P. Suprobo & E. Wahyuni (2019) Retrofitting of square reinforced concrete column by welded wire mesh jacketing with consentric axial load. IOP Conference Series: Materials Science and Engineering, 508, 012042.
XVIII. Mohamed Mady, Amr El-Ragaby & a. E. El-Salakawy (2011) Seismic Behavior of Beam-Column Joints Reinforced with GFRP Bars and Stirrups. Journal of Composites For Construction ASCE 15, 875-886.
XIX. Muhammad Masood Rafi , A. N., Faris Ali, Didier Talamona (2008) Aspects of behaviour of CFRP reinforced concrete beams in bending. Construction and Building Materials, 22, 277–285.
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EXPERIMENTAL AND NUMERICAL FATIGUE ANALYSIS OF BRASS SHAFT SPECIMEN UNDER CYCLIC BENDING MOMENTS

Authors:

Haider Abbas Luaibi, Majid Habeeb Faidh - Allah

DOI NO:

https://doi.org/10.26782/jmcms.2021.03.00001

Abstract:

Fatigue is a form of failure that occurs in structures subjected to dynamic and fluctuating stresses, where failure can occur at a stress level significantly lower than the tensile or yield strength of a static load under these circumstances. The term "fatigue" is used because, after a long period of repetitive stress or stress cycling, this form of failure typically occurs. Fatigue is important because it is the single largest cause of metal failure, estimated to account for about 90% of all metal failures; polymers and ceramics (except glasses) are also prone to this form of failure. This research is studying the failure analysis, fatigue life and endurance limit of brass metal experimental and numerical under cyclic bending moments

Keywords:

Fatigue,Cyclic,Endurance limit,Fatigue life,Brass metal,

Refference:

I. A Karolczuk., Macha E. A review of critical plane orientations in multiaxial fatigue failure criteria of metallic materials. Int J Fract 1995; 134:267–304
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V. Glinka, G. And Ince, “A Generalized Fatigue Damage Parameter for Multiaxial Fatigue Life Prediction under Proportional and Non-Proportional Loadings”, International Journal of Fatigue, 62, 34-41, 2014
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IMPACT OF BLACK HOLE ATTACK ON THE PERFORMANCE OF DYNAMIC SOURCE ROUTING AND OPTIMIZED LINK STATE ROUTING PROTOCOLS IN MANETS

Authors:

Waqas Khan, Vishwesh Laxmikant Akre, Khalid Saeed, Asif Nawaz, Tariq Bashir, Adil Khan, Naveed Jan, Sheeraz Ahmed, Zia Ullah Khan

DOI NO:

https://doi.org/10.26782/jmcms.2021.03.00002

Abstract:

Mobile Ad-Hoc Networks (MANETs) are a collection of mobile nodes which are free to move from one place to another place without a central control entity. In MANETs the nodes are dependent on each other and the communication among mobile nodes is multi-hop due to which there are security issues in the MANETs protocols. Optimized Link State Routing (OLSR) and Dynamic Source Routing (DSR) protocols are mostly used as proactive and reactive routing protocols in MANETs. This research work analyzed the performance of the OLSR and DSR protocols in the presence and absence of black hole (BH) attack in terms of throughput, end-to-end delay, packet delivery ratio (PDR), and network load in various scenarios using OPNET Modeler 14.5 simulator. The results obtained in this research show that BH attack significantly degrades the performance of both DSR and OLSR protocols but due to the reactive nature of DSR routing protocol the performance is more degraded in DSR routing protocol as compared to OLSR routing protocol in the presence of BH attack.

Keywords:

MANETs,Ad-Hoc Routing Protocols,OLSR,DSR,Malicious Nodes,Black Hole Attack,

Refference:

I. Adam, G., Kapoulas, V., Bouras, C., Kioumourtzis, G., Gkamas, A., &Tavoularis, N. (2011, October). Performance evaluation of routing protocols for multimedia transmission over mobile ad hoc networks. In Wireless and Mobile Networking Conference (WMNC), 2011 4th Joint IFIP (pp. 1-6). IEEE.
II. Ade, S. A., &Tijare, P. A. (2010). Performance comparison of AODV, DSDV, OLSR and DSR routing protocols in mobile ad hoc networks. International Journal of Information Technology and Knowledge Management, 2(2), 545-548.
III. Aggarwal, R., &Rana, S. A. (2014). Comparitative Survey on Malicious Nodes and Their Attacks in MANET. (IOSR-JCE), 16(3), (PP 93-101).
IV. Arora, N., &Barwar, N. C. (2014). Performance Analysis of Black Hole Attack on different MANET Routing Protocols. International Journal of Computer Science and Information technologies, 5(3), 4417-4419.
V. Babu, E. S., Naganjaneyulu, S., Rao, P. S., & Reddy, G. N. (2019). An Efficient Cryptographic Mechanism to Defend Collaborative Attack Against DSR Protocol in Mobile Ad hoc Networks. In Information and Communication Technology for Intelligent Systems (pp. 21-30). Springer, Singapore.
VI. Chaurasia, M., & Singh, B. P. (2018). Prevention of DOS and Routing Attack in OLSR Under MANET. In Proceedings of International Conference on Recent Advancement on Computer and Communication (pp. 287-295). Springer, Singapore.
VII. Dokurer, S., Erten, Y. M., &Acar, C. E. (2007, March). Performance analysis of ad-hoc networks under black hole attacks. In SoutheastCon, 2007. Proceedings. IEEE (pp. 148-153). IEEE.
VIII. Garg, N., & Mahapatra, R. P. (2009). MANET Security issues. IJCSNS, 9(8), 241.
IX. Jaiswal, P., & Kumar, D. R. (2012). Prevention of Black Hole Attack in MANET. IRACST–International Journal of Computer Networks and Wireless Communications (IJCNWC), ISSN, 2250-3501
X, Jamal, T., & Butt, S. A. (2018). Malicious node analysis in MANETS. International Journal of Information Technology, 1-9.
XI. Johnson, D. B., Maltz, D. A., &Broch, J. (2001). DSR: The dynamic source routing protocol for multi-hop wireless ad hoc networks. Ad hoc networking, 5, 139-172.
XII. Kaur, T., & Singh, A. (2013). Performance Evaluation of MANET with Black Hole Attack Using Routing Protocols. International Journal of Engineering Research and Applications (IJERA) ISSN, 2248(9622), 1324-1328.
XIII. Mamatha, G. S., & Sharma, D. S. (2010). A highly secured approach against attacks in MANETS. International Journal of Computer Theory and Engineering, 2(5), 1793-8201.
XIV. Mohammad, A. A. K., Mahmood, A. M., & Vemuru, S. (2019). Providing Security Towards the MANETs Based on Chaotic Maps and Its Performance. In Microelectronics, Electromagnetics and Telecommunications (pp. 145-152). Springer, Singapore.
XV. Mohammad, S. N., Singh, R. P., Dey, A., & Ahmad, S. J. (2019). ESMBCRT: Enhance Security to MANETs Against Black Hole Attack Using MCR Technique. In Innovations in Electronics and Communication Engineering (pp. 319-326). Springer, Singapore.
XVI. Mohebi, A., Kamal, E., & Scott, S. (2013). Simulation and analysis of AODV and DSR routing protocol under black hole attack. International Journal of Modern Education and Computer Science, 5(10), 19.
XVII. Mani, U., Chandrasekaran, R., & Dhulipala, V. S. (2013). Study and analysis of routing protocols in mobile ad-hoc network. Journal of Computer Science, 9(11), 1519.
XVIII. Rohal, P., Dahiya, R., &Dahiya, P. (2013). Study and analysis of throughput, delay and packet delivery ratio in MANET for topology based routing protocols (AODV, DSR and DSDV). international journal for advance research in engineering and technology, 1. (Vol. 1, pp. 54-58).
XIX. Roy A., Deb T. (2018) Performance Comparison of Routing Protocols in Mobile Ad Hoc Networks. In: Mandal J., Saha G., Kandar D., Maji A. (eds) Proceedings of the International Conference on Computing and Communication Systems. Lecture Notes in Networks and Systems, vol 24. Springer, Singapore
XX. Saddiki, K., Boukli-Hacene, S., Gilg, M., & Lorenz, P. (2018, September). Trust-Neighbors-Based to Mitigate the Cooperative Black Hole Attack in OLSR Protocol. In International Symposium on Security in Computing and Communication (pp. 117-131). Springer, Singapore.
XXI. Sajjad Muhammad, Khalid Saeed, Tariq Hussain, ArbabWaseem Abbas, Irshad Khalil, Iqtidar Ali, Nida Gul. : Impact of Jelly Fish Attackonthe Performance of DSR Routing Protocol in MANETs, J. Mech. Cont.& Math. Sci., Vol.-14, No.-4, July-August (2019) pp 132-140
XXII. Salehi, M., Samavati, H., &Dehghan, M. (2012, May). Evaluation of DSR protocol under a new Black hole attack. In Electrical Engineering (ICEE), 2012 20th Iranian Conference on (pp. 640-644). IEEE.
XXIII. Shrestha, A., &Tekiner, F. (2009, December). On MANET routing protocols for mobility and scalability. In Parallel and Distributed Computing, Applications and Technologies, 2009 International Conference on (pp. 451-456). IEEE.
XXIV. Tariq Hussain, Iqtidar Ali, Muhammad Arif, Samad Baseer, Fatima Pervez, Zia Ur Rehman. : AN INVESTIGATION OF THE PERFORMANCE OPTIMIZED LINK STATE ROUTING PROTOCOL ON THE BASIS OF MOBILITY MODELS, J. Mech. Cont.& Math. Sci., Vol.-15, No.-9, September (2020) pp 306-327.
XXV. Vamsi, P. R., & Kant, K. (2017). Generalized trust model for cooperative routing in MANETs. Wireless Personal Communications, 97(3), 4385-4412.

A NEW AND EFFICIENT CENTROIDAL MEAN DERIVATIVE-BASED TRAPEZOIDAL SCHEME FOR NUMERICAL CUBATURE

Authors:

Kamran Malik , Muhammad Mujtaba Shaikh, Kashif Memon, Muhammad Saleem Chandio, Abdul Wasim Shaikh

DOI NO:

https://doi.org/10.26782/jmcms.2021.03.00003

Abstract:

This research presents a new and efficient Centroidal mean derivative-based numerical cubature scheme which has been proposed for the accurate evaluation of double integrals under finite range. The proposed modification is based on the Trapezoidal-type quadrature and cubature rules. The approximate values can only be obtained for some important applications to evaluate the complex double integrals. Higher precision and order of accuracy could be achieved by the proposed scheme. The schemes, in basic and composite forms, with local and global error terms are presented with necessary supporting arguments with their performance evaluation against conventional Trapezoid rule through some numerical experiments. The simultaneously observed error distributions of the proposed schemes are found to be lower than the conventional Trapezoidal cubature scheme in composite form

Keywords:

Cubature,Double integrals,Centroidal mean Derivative-based scheme,Precision,Order of accuracy,Local and global errors,Trapezoid,

Refference:

IV. Burden R. L., J. D. Faires, Numerical Analysis, Brooks/Cole, Boston, Mass, USA, 9th edition, 2011.
V. Burg. C. O. E., Derivative-based closed Newton-cotes numerical quadrature, Applied Mathematics and Computations, 218 (2012), 7052-7065.
VI. Dehghan M., M. Masjed-Jamei and M. R. Eslahchi, The semi-open Newton- Cotes quadrature rule and its numerical improvement, Applied Mathematics and Computations, 171 (2005) 1129-1140.
VII. Dehghan M., M. Masjed-Jamei, and M. R. Eslahchi, “On numerical improvement of closed Newton-Cotes quadrature rules,” Applied Mathematics and Computation, vol. 165, no. 2,pp. 251–260, 2005.
VIII. Dehghan M., M. Masjed-Jamei, and M. R. Eslahchi, “On numerical improvement of open Newton-Cotes quadrature rules,” Applied Mathematics and Computation, vol. 175, no. 1, pp.618–627, 2006.
IX. Jain M. K., S. R. K. Iyengar and R. K. Jain, Numerical Methods for Scientific and Computation, New Age International (P) Limited, Fifth Edition, 2007.
X. Malik K., Shaikh, M. M., Chandio, M. S. and Shaikh, A. W. Some new and efficient derivative-based schemes for numerical cubature., :J. Mech. Cont. & Math. Sci., Vol. 15, No.11, pp. 67-78, 2020.
XI. Memon K., M. M. Shaikh, M. S. Chandio, A. W. Shaikh, “A Modified Derivative-Based Scheme for the Riemann-Stieltjes Integral”, 52(01) 37-40 (2020).
XII. Pal M., Numerical Analysis for Scientists and Engineers: theory and C programs, Alpha Science, Oxford, UK, 2007.
XIII. Petrovskaya N., E. Venturino, “Numerical integration of sparsely sampled data,” Simulation Modelling Practice and Theory,vol. 19, no. 9, pp. 1860–1872, 2011.
XIV. Ramachandran T. (2016), D. Udayakumar and R. Parimala, “Comparison of Arithmetic Mean, Geometric Mean and Harmonic Mean Derivative-Based Closed Newton Cotes Quadrature“, Nonlinear Dynamics and Chaos Vol. 4, No. 1, 2016, 35-43 ISSN: 2321 – 9238.
XV. Sastry S.S., Introductory methods of numerical analysis, Prentice-Hall of India, 1997.

XVI. Shaikh, M. M., (2019), “Analysis of Polynomial Collocation and Uniformly Spaced Quadrature Methods for Second Kind Linear Fredholm Integral Equations – A Comparison”. Turkish Journal of Analysis and NumberTheory,7(4)91-97. doi: 10.12691/tjant-7-4-1.
XVII. Shaikh, M. M., M. S. Chandio and A. S. Soomro, (2016), “A Modified Four-point Closed Mid-point Derivative Based Quadrature Rule for Numerical Integration”, Sindh University Research Journal-SURJ (Science Series) 48(2): 389-392.
XVIII. Zafar F., S. Saleem and C. O. E. Burg, New derivative based open Newton-Cotes quadrature rules, Abstract and Applied Analysis, Volume 2014, Article ID 109138, 16 pages, 2014.
XIX. Zhao, W., and H. Li, (2013) “Midpoint Derivative- Based Closed Newton-Cotes Quadrature”, Abstract And Applied Analysis, Article ID 492507.
XX. Zhao, W., Z. Zhang, and Z. Ye, (2014), “Midpoint Derivative-Based Trapezoid Rule for the Riemann- Stieltjes Integral”, Italian Journal of Pure and Applied Mathematics, 33: 369-376.

AN EFFICIENT TRAPEZOIDAL SCHEME FOR NUMERICAL CUBATURE WITH HERONIAN MEAN DERIVATIVE

Authors:

Kamran Malik , Muhammad Mujtaba Shaikh, Kashif Memon, Muhammad Saleem Chandio, Abdul Wasim Shaikh

DOI NO:

https://doi.org/10.26782/jmcms.2021.03.00004

Abstract:

This study focuses on the Heronian mean derivative-based numerical cubature scheme to better evaluate double integrals' infinite limits. The proposed modifications rely on the Trapezoidal-type quadrature and cubature schemes. The aforementioned proposed scheme is important to numerically evaluate the complex double integrals, where the exact value is not available but the approximate values can only be obtained. With regards to higher precision and order of accuracy, the proposed Heronian derivative-based double integral scheme provides efficient results. The discussed scheme, in basic and composite forms, with local and global error terms is presented with necessary proofs with their performance evaluation against conventional Trapezoid rule through some numerical experiments. The consequently observed error distributions of the aforementioned scheme are found to be lower than the conventional Trapezoidal cubature scheme in composite form

Keywords:

Cubature,Double integrals,Heronian mean Derivative-based scheme,Precision,Order of accuracyLocal and global errors,Local and global errors,Trapezoid,

Refference:

I. Babolian E., M. Masjed-Jamei and M. R. Eslahchi, On numerical improvement of Gauss-Legendre quadrature rules, Applied Mathematics and Computations, 160(2005) 779-789.
II. Bailey D. H. and J. M. Borwein, “High precision numerical integration: progress and challenges,” Journal of Symbolic Computation ,vol. 46, no. 7, pp. 741–754, 2011.
III. Bhatti, A. A., M.S. Chandio, R.A. Memon and M. M. Shaikh, (2019), “A Modified Algorithm for Reduction of Error in Combined Numerical Integration”, Sindh University Research Journal-SURJ (Science Series) 51(4): 745-750.
IV. Burden R. L., J. D. Faires, Numerical Analysis, Brooks/Cole, Boston, Mass, USA, 9th edition, 2011.
V. Burg. C. O. E., Derivative-based closed Newton-cotes numerical quadrature, Applied Mathematics and Computations, 218 (2012), 7052-7065.
VI. Dehghan M., M. Masjed-Jamei and M. R. Eslahchi, The semi-open Newton- Cotes quadrature rule and its numerical improvement, Applied Mathematics and Computations, 171 (2005) 1129-1140.
VII. Dehghan M., M. Masjed-Jamei, and M. R. Eslahchi, “On numerical improvement of closed Newton-Cotes quadrature rules,” Applied Mathematics and Computation, vol. 165, no. 2,pp. 251–260, 2005.
VIII. Dehghan M., M. Masjed-Jamei, and M. R. Eslahchi, “On numerical improvement of open Newton-Cotes quadrature rules,” Applied Mathematics and Computation, vol. 175, no. 1, pp.618–627, 2006.
IX. Jain M. K., S. R. K. Iyengar and R. K. Jain, Numerical Methods for Scientific and Computation, New Age International (P) Limited, Fifth Edition, 2007.
X. Malik K., Shaikh, M. M., Chandio, M. S. and Shaikh, A. W. Some new and efficient derivative-based schemes for numerical cubature., : J. Mech. Cont. & Math. Sci., Vol. 15, No.11, pp. 67-78, 2020.
XI. Memon K., M. M. Shaikh, M. S. Chandio, A. W. Shaikh, “A Modified Derivative-Based Scheme for the Riemann-Stieltjes Integral”, 52(01) 37-40 (2020).
XII. Pal M., Numerical Analysis for Scientists and Engineers: theory and C programs, Alpha Science, Oxford, UK, 2007.
XIII. Petrovskaya N., E. Venturino, “Numerical integration of sparsely sampled data,” Simulation Modelling Practice and Theory,vol. 19, no. 9, pp. 1860–1872, 2011.

XIV. Ramachandran T. (2016), D. Udayakumar and R. Parimala, “Comparison of Arithmetic Mean, Geometric Mean and Harmonic Mean Derivative-Based Closed Newton Cotes Quadrature“, Nonlinear Dynamics and Chaos Vol. 4, No. 1, 2016, 35-43 ISSN: 2321 – 9238.
XV. Sastry S.S., Introductory methods of numerical analysis, Prentice-Hall of India, 1997.
XVI. Shaikh, M. M., (2019), “Analysis of Polynomial Collocation and Uniformly Spaced Quadrature Methods for Second Kind Linear Fredholm Integral Equations – A Comparison”. Turkish Journal of Analysis and NumberTheory,7(4)91-97. doi: 10.12691/tjant-7-4-1.
XVII. Shaikh, M. M., M. S. Chandio and A. S. Soomro, (2016), “A Modified Four-point Closed Mid-point Derivative Based Quadrature Rule for Numerical Integration”, Sindh University Research Journal-SURJ (Science Series) 48(2): 389-392.
XVIII. Zafar F., S. Saleem and C. O. E. Burg, New derivative based open Newton-Cotes quadrature rules, Abstract and Applied Analysis, Volume 2014, Article ID 109138, 16 pages, 2014.
XIX. Zhao, W., and H. Li, (2013) “Midpoint Derivative- Based Closed Newton-Cotes Quadrature”, Abstract And Applied Analysis, Article ID 492507.
XX. Zhao, W., Z. Zhang, and Z. Ye, (2014), “Midpoint Derivative-Based Trapezoid Rule for the Riemann- Stieltjes Integral”, Italian Journal of Pure and Applied Mathematics, 33: 369-376.

HERONIAN MEAN DERIVATIVE-BASED SIMPSON’S-TYPE SCHEME FOR RIEMANN-STIELTJES INTEGRAL

Authors:

Kashif Memon , Muhammad Mujtaba Shaikh, Kamran Malik, Muhammad Saleem Chandio, Abdul Wasim Shaikh

DOI NO:

https://doi.org/10.26782/jmcms.2021.03.00005

Abstract:

In this paper, a new heronian mean derivative-based quadrature scheme of Simpson’s 1/3-type is proposed for the approximation of the Riemann-Stieltjes integral (RS-integral). Theorems are proved related to the basic form, composite form, local and global errors of the new scheme for the RS-integral. The reduction of the new proposed scheme is verified using g(t) = t for Riemann integral. The theoretical results of the new proposed scheme have been proved by experimental work using programming in MATLAB against existing schemes. The order of accuracy, computational cost and average CPU time (in seconds) of the new proposed scheme are determined. The results obtained show the effectiveness of the proposed scheme compared to the existing schemes.

Keywords:

Quadrature rule,Riemann-Stieltjes,Simpson’s 1/3 rule,Composite form,Local error,Global error,Cost-effectiveness,Time-efficiency,Heronian Mean,

Refference:

I. Bartle, R.G. and Bartle, R.G., The elements of real analysis, (Vol. 2). John Wiley & Sons, 1964.
II. Bhatti AA, Chandio MS, Memon RA and Shaikh MM, A Modified Algorithm for Reduction of Error in Combined Numerical Integration, Sindh University Research Journal-SURJ (Science Series) 51.4, (2019): 745-750.
III. Burden, R.L., Faires, J.D., Numerical Analysis, Brooks/Cole, Boston, Mass, USA, 9th edition, 2011.
IV. Dragomir, S.S., and Abelman S., Approximating the Riemann-Stieltjes integral of smooth integrands and of bounded variation integrators, Journal of Inequalities and Applications, 2013.1 (2013), 154.
V. Malik K., Shaikh, M. M., Chandio, M. S. and Shaikh, A. W. Error analysis of closed Newton-Cotes cubature schemes for double integrals. : J. Mech. Cont. & Math. Sci., 15 (11): 95-107, 2020.
VI. Malik K., Shaikh, M. M., Chandio, M. S. and Shaikh, A. W. Some new and efficient derivative-based schemes for numerical cubature. : J. Mech. Cont. & Math. Sci.,15 (10): 67-78, 2020.
VII. Mastoi, Adnan Ali, Muhammad Mujtaba Shaikh, and Abdul Wasim Shaikh. A new third-order derivative-based iterative method for nonlinear equations. : J. Mech. Cont. & Math. Sci., 15 (10): 110-123, 2020.
VIII. Memon K, Shaikh MM, Chandio MS and Shaikh AW, A Modified Derivative-Based Scheme for the Riemann-Stieltjes Integral, Sindh University Research Journal-SURJ (Science Series) 52.1, (2020): 37-40.
IX. Memon K., Shaikh, M. M., Chandio, M. S. and Shaikh, A. W. A new and efficient Simpson’s 1/3-type quadrature rule for Riemann-Stieltjes integral. : J. Mech. Cont. & Math. Sci., 15 (11): 132-148, 2020.
X. Memon, A. A., Shaikh, M. M., Bukhari, S. S. H., & Ro, J. S. Look-up Data Tables-Based Modeling of Switched Reluctance Machine and Experimental Validation of the Static Torque with Statistical Analysis. Journal of Magnetics, 25(2): 233-244, 2020.
XI. Mercer, P.R., Hadamard’s inequality and Trapezoid rules for the Riemann-Stieltjes integral, Journal of Mathematica Analysis and Applications, 344 (2008), 921-926.
XII. Mercer, P.R., Relative convexity and quadrature rules for the Riemann-Stieltjes integral, Journal of Mathematica inequality, 6 (2012), 65-68.
XIII. Protter, M.H. and Morrey, C.B., A First Course in Real Analysis . Springer, New York, NY, 1977.
XIV. Ramachandran Thiagarajan, Udayakumar.D, Parimala .R, Geometric mean derivative-based closed Newton-Cotes quadrature, International Journal of Pure & Engineering Mathematics, 4, 107-116, April 2016.
XV. Ramachandran Thiagarajan, Udayakumar.D, Parimala .R, Harmonic mean derivative-based closed Newton-Cotes quadrature, IOSR-Journal of Mathematics, 12, 36-41, May-June 2016.
XVI. Ramachandran Thiagarajan, Udayakumar.D, Parimala .R, Heronian mean derivative- based closed Newton cotes quadrature, International Journal of Mathematical Archive, 7, 53-58, July 2016.
XVII. Ramachandran Thiagarajan, Parimala .R, Centroidal mean derivative–based closed Newton cotes quadrature, International Journal of Science and Research, 5, 338-343, August 2016.
XVIII. Shaikh, MM., MS Chandio and AS Soomro, A Modified Four-point Closed Mid-point Derivative Based Quadrature Rule for Numerical Integration, Sindh University Research Journal-SURJ (Science Series), 48.2, 2016.
XIX. Shaikh, Muhammad Mujtaba, Shafiq-ur-Rehman Massan, and Asim Imdad Wagan. “A new explicit approximation to Colebrook’s friction factor in rough pipes under highly turbulent cases.” International Journal of Heat and Mass Transfer 88 (2015): 538-543.
XX. Shaikh, Muhammad Mujtaba, Shafiq-ur-Rehman Massan, and Asim Imdad Wagan. “A sixteen decimal places’ accurate Darcy friction factor database using non-linear Colebrook’s equation with a million nodes: A way forward to the soft computing techniques.” Data in brief 27 (2019): 104733.
XXI. Shaikh, Muhammad Mujtaba. “Analysis of Polynomial Collocation and Uniformly Spaced Quadrature Methods for Second Kind Linear Fredholm Integral Equations–A Comparison.” Turkish Journal of Analysis and Number Theory 7.4 (2019): 91-97.
XXII. Umar, Sehrish, Muhammad Mujtaba Shaikh, and Abdul Wasim Shaikh. A new quadrature-based iterative method for scalar nonlinear equations. : J. Mech. Cont. & Math. Sci., 15 (10): 79-93, 2020.
XXIII. Zhao, W., and H. Li, Midpoint Derivative-Based Closed Newton-Cotes Quadrature, Abstract And Applied Analysis, Article ID 492507, (2013).
XXIV. Zhao, W., Z. Zhang, and Z. Ye, Composite Trapezoid rule for the Riemann-Stieltjes Integral and its Richardson Extrapolation Formula, Italian Journal of Pure and Applied Mathematics, 35 (2015), 311-318.
XXV. Zhao, W., Z. Zhang, and Z. Ye, Midpoint Derivative-Based Trapezoid Rule for the Riemann-Stieltjes Integral, Italian Journal of Pure and Applied Mathematics, 33, (2014), 369-376.

EFFICIENT DERIVATIVE-BASED SIMPSON’S 1/3-TYPE SCHEME USING CENTROIDAL MEAN FOR RIEMANN-STIELTJES INTEGRAL

Authors:

Kashif Memon , Muhammad Mujtaba Shaikh, Kamran Malik, Muhammad Saleem Chandio, Abdul Wasim Shaikh

DOI NO:

https://doi.org/10.26782/jmcms.2021.03.00006

Abstract:

In this paper, a new efficient derivative-based quadrature scheme of Simpson’s 1/3-type is proposed using the centroidal mean for the approximation of Riemann-Stieltjes integral (RS-integral). Theorems are proved related to the basic form, composite form, local and global errors of the new scheme for the RS-integral. The reduction of the new proposed scheme is verified using g(t) = t for Riemann integral. The theoretical results of new proposed scheme have been proved by experimental work using programming in MATLAB against existing schemes. The order of accuracy, computational cost and average CPU time (in seconds) of the new proposed scheme are determined. The results obtained show the effectiveness of the proposed scheme compared to the existing schemes.

Keywords:

Quadrature rule,Riemann-Stieltjes integral,Centroidal Mean,Simpson’s 1/3 rule,Composite form,Local error,Global error,Cost-effectiveness,Time-efficiency,

Refference:

I. Bartle, R.G. and Bartle, R.G., The elements of real analysis, (Vol. 2). John Wiley and Sons, 1964.

II. Bhatti AA, Chandio MS, Memon RA and Shaikh MM, A Modified Algorithm for Reduction of Error in Combined Numerical Integration, Sindh University Research Journal-SURJ (Science Series) 51.4, (2019): 745-750.
III. Burden, R.L., Faires, J.D., Numerical Analysis, Brooks/Cole, Boston, Mass, USA, 9th edition, 2011.
IV. Dragomir, S.S., and Abelman S., Approximating the Riemann-Stieltjes integral of smooth integrands and of bounded variation integrators, Journal of Inequalities and Applications, 2013.1 (2013), 154.
V. Malik K., Shaikh, M. M., Chandio, M. S. and Shaikh, A. W. Error analysis of closed Newton-Cotes cubature schemes for double integrals: J. Mech. Cont. & Math. Sci., 15 (11): 95-107, 2020.
VI. Malik K., Shaikh, M. M., Chandio, M. S. and Shaikh, A. W. Some new and efficient derivative-based schemes for numerical cubature. : J. Mech. Cont. & Math. Sci., 15 (10): 67-78, 2020.
VII. Mastoi, Adnan Ali, Muhammad Mujtaba Shaikh, and Abdul Wasim Shaikh. A new third-order derivative-based iterative method for nonlinear equations. : J. Mech. Cont. & Math. Sci., 15 (10): 110-123, 2020.
VIII. Memon K, Shaikh MM, Chandio MS and Shaikh AW, A Modified Derivative-Based Scheme for the Riemann-Stieltjes Integral, Sindh University Research Journal-SURJ (Science Series) 52.1, (2020): 37-40.
IX. Memon K., Shaikh, M. M., Chandio, M. S. and Shaikh, A. W. A new and efficient Simpson’s 1/3-type quadrature rule for Riemann-Stieltjes integral. : J. Mech. Cont. & Math. Sci., 15 (11): 132-148, 2020.
X. Memon, A. A., Shaikh, M. M., Bukhari, S. S. H., & Ro, J. S. Look-up Data Tables-Based Modeling of Switched Reluctance Machine and Experimental Validation of the Static Torque with Statistical Analysis. Journal of Magnetics, 25(2): 233-244, 2020.
XI. Mercer, P.R., Hadamard’s inequality and Trapezoid rules for the Riemann-Stieltjes integral, Journal of Mathematica Analysis and Applications, 344 (2008), 921-926.
XII. Mercer, P.R., Relative convexity and quadrature rules for the Riemann-Stieltjes integral, Journal of Mathematica inequality, 6 (2012), 65-68.
XIII. Protter, M.H. and Morrey, C.B., A First Course in Real Analysis . Springer, New York, NY, 1977.
XIV. Ramachandran Thiagarajan, Udayakumar.D, Parimala .R, Geometric mean derivative-based closed Newton-Cotes quadrature, International Journal of Pure & Engineering Mathematics, 4, 107-116, April 2016.
XV. Ramachandran Thiagarajan, Udayakumar.D, Parimala .R, Harmonic mean derivative-based closed Newton-Cotes quadrature, IOSR-Journal of Mathematics, 12, 36-41, May-June 2016.
XVI. Ramachandran Thiagarajan, Udayakumar.D, Parimala .R, Heronian mean derivative- based closed Newton cotes quadrature, International Journal of Mathematical Archive, 7, 53-58, July 2016.

XVII. Ramachandran Thiagarajan, Parimala .R, Centroidal mean derivative–based closed Newton cotes quadrature, International Journal of Science and Research, 5, 338-343, August 2016.
XVIII. Shaikh, MM., MS Chandio and AS Soomro, A Modified Four-point Closed Mid-point Derivative Based Quadrature Rule for Numerical Integration, Sindh University Research Journal-SURJ (Science Series), 48.2, 2016.
XIX. Shaikh, Muhammad Mujtaba, Shafiq-ur-Rehman Massan, and Asim Imdad Wagan. “A new explicit approximation to Colebrook’s friction factor in roughpipes under highly turbulent cases.” International Journal of Heat and MassTransfer 88 (2015): 538-543.
XX. Shaikh, Muhammad Mujtaba, Shafiq-ur-Rehman Massan, and Asim Imdad Wagan. “A sixteen decimal places’ accurate Darcy friction factor database using non-linear Colebrook’s equation with a million nodes: A way forward to the soft computing techniques.” Data in brief 27 (2019): 104733.
XXI. Shaikh, Muhammad Mujtaba. “Analysis of Polynomial Collocation and Uniformly Spaced Quadrature Methods for Second Kind Linear Fredholm Integral Equations–A Comparison.” Turkish Journal of Analysis and Number Theory 7.4 (2019): 91-97
XXII. Umar, Sehrish, Muhammad Mujtaba Shaikh, and Abdul Wasim Shaikh. A new quadrature-based iterative method for scalar nonlinear equations. : J. Mech. Cont. & Math. Sci., 15 (10): 79-93, 2020.
XXIII. Zhao, W., and H. Li, Midpoint Derivative-Based Closed Newton-Cotes Quadrature, Abstract And Applied Analysis, Article ID 492507, (2013).
XXIV. Zhao, W., Z. Zhang, and Z. Ye, Composite Trapezoid rule for the Riemann-Stieltjes Integral and its Richardson Extrapolation Formula, Italian Journal of Pure and Applied Mathematics, 35 (2015), 311-318.
XXV. Zhao, W., Z. Zhang, and Z. Ye, Midpoint Derivative-Based Trapezoid Rule for the Riemann-Stieltjes Integral, Italian Journal of Pure and Applied Mathematics, 33, (2014), 369-376.