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A NEW AND EFFICIENT SIMPSON’S 1/3-TYPE QUADRATURE RULE FOR RIEMANN-STIELTJES INTEGRAL

Authors:

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

DOI NO:

https://doi.org/10.26782/jmcms.2020.11.00012

November 30, 2020

Abstract:

In this research paper, a new derivative-free Simpson 1/3-type quadrature scheme has been proposed for the approximation of the Riemann-Stieltjes integral (RSI). The composite form of the proposed scheme on the RSI has been derived using the concept of precision. The theorems concerning basic form, composite form, local and global errors of the new scheme have been proved theoretically. For the trivial case of the integrator in the proposed RS scheme, successful reduction to the corresponding Riemann scheme is proved. The performance of the proposed scheme has been tested by numerical experiments using MATLAB on some test problems of RS integrals from literature against some existing schemes. The computational cost, the order of accuracy and average CPU times (in seconds) of the discussed rules have been computed to demonstrate cost-effectiveness, time-efficiency and rapid convergence of the proposed scheme under similar conditions.

Keywords:

Quadrature rule,Riemann-Stieltjes,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 & 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. : Some new and efficient derivative-based schemes for numerical cubature. Journal of Mechanics of Continua and Mechanical Sciences, Vol.-15, No.-10, October (2020) pp: 67-78, 2020.
VI. 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.
VII. Memon, A. A., Shaikh, M. M., Bukhari, S. S. H., & Ro, J. S. (2020). 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.
VIII. Mercer, P.R., Hadamard’s inequality and Trapezoid rules for the Riemann-Stieltjes integral, Journal of Mathematica Analysis and Applications, 344 (2008), 921-926.
IX. Mercer, P.R., Relative convexity and quadrature rules for the Riemann-Stieltjes integral, Journal of Mathematica inequality, 6 (2012), 65-68.
X. Malik Kamran, Muhammad Mujtaba Shaikh, Muhammad Saleem Chandio, Abdul Wasim Shaikh, : SOME NEW AND EFFICIENT DERIVATIVE-BASED SCHEMES FOR NUMERICAL CUBATURE, J. Mech. Cont. & Math. Sci., Vol.-15, No.-10, October (2020) pp 67-78.
XI. Mokhtar A. Abd El Naby, Nabil T. Mohammed El Dabe, : Numerical Solution And Global Error Estimation of Peristaltic Motion Of A Jhonson-Segalman Fluid With Heat and Mass Transfer In A Planer Channel, J. Mech. Cont. & Math. Sci., Vol – 2 No -1, July (2007) 16-35
XII. Protter, M.H. and Morrey, C.B., A First Course in Real Analysis . Springer, New York, NY, 1977.
XIII. Ramachandran, T., D. Udayakumar, and R. Parimala, Comparison of Arithmetic Mean, Geometric Mean and Harmonic Mean Derivative-Based Closed Newton Cote Quadrature, Progress in Nonlinear dynamics and Chaos, 4 (2016), 35-43.
XIV. 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).
XV. Shaikh, M. M. “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
XVI. Zafar, F., S. Saleem and C. O. E. Burg, New Derivative Based Open Newton-Cotes Quadrature Rules, Abstract and Applied Analysis, 2014 (2014), Article ID 109138, 16 Pages. doi:10.1155/2014/109138.
XVII. Zhao, W., and H. Li, Midpoint Derivative-Based Closed Newton-Cotes Quadrature, Abstract And Applied Analysis, Article ID 492507, (2013).
XVIII. 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.
XIX. 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.

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Journal Vol – 15 No -11, November 2020

A PIONEERING AND COMPREHENSIVE DATABASE OF BALANCED AND UNBALANCED TRANSPORTATION PROBLEMS FOR READY PERFORMANCE EVALUATION OF EXISTING AND NEW METHODS

Authors:

Huzoor Bux Kalhoro , Hafeezullah Abdulrehman, Muhammad Mujtaba Shaikh, Abdul Sattar Soomro

DOI NO:

https://doi.org/10.26782/jmcms.2020.11.00013

December 1, 2020

Abstract:

In this paper, we present a comprehensive database of the data tables of some important transportation problems from literature, and experience with the proposition of new initial basic feasible (IBF) solution methods for the transportation problems. The paper contains a comprehensive database of 140 transportation problems, of which 103 are balanced, 25 are unbalanced and 12 are from research papers. The detailed description of the varying-nature test problems is described, and the optimal solutions of the 140 problems have been obtained by using the TORA software with the modified distribution (MODI) method. The algorithms of three methods: North-West-Corner (NWCM), Least cost (LCM) and Vogel’s approximation (VAM) have been used for IBF solutions. The final optimal results are also quoted for the ready reference of researchers and practitioners. The database of problems and their optimal solutions will be a great aid to researchers and practitioners working with the existing and new methods for solving transportation problems. A pioneering investigation of the performance evaluation of NWCM, LCM and VAM has also been conducted as a benchmark for the similar assessment of other existing and forthcoming IBF and /or optimal solution methods for the transportation problems.  

Keywords:

Transportation problem,optimal solution,MODI method,TORA software,Minimum cost,performance evaluation,

Refference:

I. Adlakha, Veena, and Krzysztof Kowalski. “Alternate solutions analysis for transportation problems.” Journal of Business & Economics Research 7.11 (2009): 41-49.
II. Bhan, Veer, Ashfaque Ahmed Hashmani, and Muhammad Mujtaba Shaikh. “A new computing perturb-and-observe-type algorithm for MPPT in solar photovoltaic systems and evaluation of its performance against other variants by experimental validation.” Scientia Iranica 26, no. Special Issue on machine learning, data analytics, and advanced optimization techniques in modern power systems [Transactions on Computer Science & Engineering and Electrical Engineering (D)] (2019): 3656-3671.
III. Chungath Linesh, “Comparison of Transportation Problems Solved by Vogel’s Approximation Method (VAM-1958), Revised Distribution Method (RDI -2013) & The New Method”, available online, 2004 @ https://www.academia.edu/1137498
IV. Das, Utpal Kanti, et al. “Logical development of vogel’s approximation method (LD-VAM): an approach to find basic feasible solution of transportation problem.” International Journal of Scientific & Technology Research 3.2 (2014): 42-48.
V. Deshmukh, N. M. “An innovative method for solving transportation problem.” International Journal of Physics and Mathematical Sciences 2.3 (2012): 86-91.
VI. Goyal, S. K. “Improving VAM for unbalanced transportation problems.” Journal of the Operational Research Society 35.12 (1984): 1113-1114.
VII. Hakim, M. A. “An alternative method to find initial basic feasible solution of a transportation problem.” Annals of pure and applied mathematics 1.2 (2012): 203-209.
VIII. Islam Md Amirul, Aminur Rehman Khan, Sharif Uddin M and Abdul Malek M Islam. “Determination of basic feasible solution of transportation problem: a new approach.” Jahangirnagar University Journal of Science 35.1 (2012): 101-108.
IX. Jamali, S., Shaikh, M. M., & Soomro, A. S. (2019). Overview of Optimality of New Direct Optimal Methods for the Transportation Problems. Asian Research Journal of Mathematics, 15(4), 1-10.
X. Jamali S., Soomro, A. S., & Shaikh, M. M. (2020). The Minimum Demand Method – A New and Efficient Initial Basic Feasible Solution Method for Transportation Problems. Journal of Mechanics of Continua and Mathematical Sciences, 15 (10), 94-105.
XI. Korukoğlu, Serdar, and Serkan Ballı. “A Improved Vogel’s Approximation Method for the Transportation Problem.” Mathematical and Computational Applications 16.2 (2011): 370-381.
XII. Mamidi, Pushpa Latha. “Ones method for finding an optimal solution for transportation problem.” In Proceedings International Conference On Advances In Engineering And Technology, International Association of Engineering & Technology for Skill Development, 41-45, ISBN NO: 978 – 1503304048,
XIII. Massan, S.-u-R., Wagan, A. I., & Shaikh, M. M.. “A new metaheuristic optimization algorithm inspired by human dynasties with an application to the wind turbine micrositing problem.” Applied Soft Computing 90 (2020): 106176.
XIV. M. Wali Ullah, Rizwana Kawser, M. Alhaz Uddin, : A DIRECT ANALYTICAL METHOD FOR FINDING AN OPTIMAL SOLUTION FOR TRANSPORTATION PROBLEMS, J. Mech.Cont. & Math. Sci., Vol.-9, No.-2, January (2015) Pages 1311-1320.
XV. M. A. Hossen, Farjana Binte Noor, Transportation Cost Effective named Maximum Cost, Corresponding Row and Column minima (MCRCM) Algorithm for Transportation Problem, J. Mech. Cont. & Math. Sci., Vol.-14, No.-1, January-February (2019) pp 241-249.
XVI. Pandian, P., and G. Natarajan. “A new method for finding an optimal solution for transportation problems.” International J. of Math. Sci. and Engg. Appls 4 (2010): 59-65.
XVII. Pandian P. and Natarajan G. “A new approach for solving transportation problems with mixed constraints”, Journal of Physical Sciences 14 (2010): 53-61.
XVIII. Quddoos, Abdul, Shakeel Javaid, and Mohd Massod Khalid. “A new method for finding an optimal solution for transportation problems.” International Journal on Computer Science and Engineering 4.7 (2012): 1271.
XIX. Shaikh, Muhammad Mujtaba; Soomro, Abdul Sattar; Kalhoro, Huzoor Bux (2020), “Comprehensive database of test transportation problems (balanced and unbalanced)”, Mendeley Data, V1, doi: 10.17632/b73b5kmcwm.1

XX. Sharma, S. D., Sharma Himanshu Operations Research, Kedar Nath Ram Nath, 2010
XXI. Soomro, A.S., S. Jamali, and M. M. Shaikh. “On Non-Optimality of Direct Exponential Approach Method for Solution of Transportation Problems.” Sindh University Research Journal-SURJ (Science Series) 49.1 (2017): 183-188
XXII. Soomro, Abdul Sattar, Gurudeo Anand Tularam, and Ghulam Murtaa Bhayo. “A comparative study of initial basic feasible solution methods for transportation problems.” Mathematical Theory and Modeling 4.1 (2014): 11-18.
XXIII. Soomro, Abdul Sattar, Muhammad Junaid, and Gurudev Anand Tularam. “Modified Vogel’s Approximation Method for Solving Transportation Problems.” Mathematical Theory and Modeling 5.4 (2015): 32-42.
XXIV. Sudhakar, V. J., N. Arunsankar, and T. Karpagam. “A new approach for finding an optimal solution for transportation problems.” European journal of scientific Research 68.2 (2012): 254-257.
XXV. Taha, Hamdy A. Operations research: An introduction (for VTU). Pearson Education India, 2005.
XXVI. Unit 1, Lesson 15: “Methods for finding initial solution for a transportation problem” @ https://www.coursehero.com/file/10473072/3-TransportationProblem/
XXVII. Vannan, S. Ezhil, and S. Rekha. “A New Method for Obtaining an Optimal Solution for Transportation Problems.” International Journal of Engineering and Advanced Technology 2 (2013).
XXVIII. Winston, Wayne L. “Transportation, Assignment, and Transshipment Problems.” Operations Research Applications and Algorithms, Duxbury Press, California (1994): 338.
XXIX. Yousaf, M., Shaikh M. M., & Shaikh A. W. (2020). Some Efficient Mathematical Programming Techniques for Balancing Equations of Complex Chemical Reactions. Journal of Mechanics of Continua and Mathematical Sciences, 15 (10), 53-66.

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Journal Vol – 15 No -11, November 2020

ADIATION SHIELDING EFFECT OF BASALT CONCRETE; AN EXPERIMENTAL APPROACH

Authors:

Engr. Furqan Wali, Manzoor Khan, Jahanzeb Khan, Maaz Ahmad, S.Ali Raza

DOI NO:

https://doi.org/10.26782/jmcms.2020.11.00014

December 1, 2020

Abstract:

This paper presents an assessment of gamma radiation performance, specifically in terms of attenuation energy, of concrete containing coarse aggregate having different physical and chemical properties. Basalt being heavier and somehow having high specific gravity is likely to have a good performance against gamma radiation. Through this paper, the author has made a comparison between the concrete having different coarse aggregates, normal aggregate phase and basaltic aggregate phase by evaluating the attenuation energies of both the phases at the Institute of Radiotherapy and Nuclear Medicine (IRNUM) Peshawar. Also, the water to cement ratio (W/C) for both the phases was distinguished i.e. 3.5 and 5.7 to make the results more promising and enabling to make the comparison effective. The test was likely to be conducted on Molds having 10 cm by 10 cm cross-section of each W/C ratio with varying thickness of about 2cm and will lead up to 10cm. The detecting device used was a phoenix teletherapy machine operating with a former type ionization chamber having an energy of 1.25 MeV. The source of radiation was Cobalt 60. The results indicated that basalt despite having strong physical properties is insufficient to be used for Gamma shielding. The two materials vary very little, so it is negligible to be used for a specific reason.

Keywords:

Basalt rock,Cobalt 60,W/C,Phoenix Teletherapy machine (PTW),

Refference:

I. Asad-ur-Rehman Khan, Tatheer Zahra, : Elasto-damage Modeling of Concrete Subjected to Proportionate and Non-proportionate Multiaxial State of Stress, J. Mech. Cont. & Math. Sci., Vol.-14, No.-2, March-April (2019) pp 7-26.
II. Abdo, W. Kansouh and R. Megahid, “Investigation of Radiation Attenuation Properties for Baryte Concrete”, Japanese Journal of Applied Physics, vol. 41, no. 1, 12, pp. 7512-7517, 2002. Available: 10.1143/jjap.41.7512 [Accessed 8 October 2020].
III. A. El-Sayed Abdo, M. Ali and M. Ismail, “Influence of magnetite and boron carbide on radiation attenuation of cement–fiber/composite”, Annals of Nuclear Energy, vol. 30, no. 4, pp. 391-403, 2003. Available: 10.1016/s0306-4549(02)00074-9.
IV. M. Kharita, S. Yousef and M. AlNassar, “The effect of carbon powder addition on the properties of hematite radiation shielding concrete”, Progress in Nuclear Energy, vol. 51, no. 2, pp. 388-392, 2009. Available: 10.1016/j.pnucene.2008.10.002 [Accessed 8 October 2020].
V. C. Lee, Y. Lee and K. Lee, “Cracking effect on gamma-ray shielding performance in concrete structure”, Progress in Nuclear Energy, vol. 49, no. 4, pp. 303-312, 2007. Available: 10.1016/j.pnucene.2007.01.006 [Accessed 8 October 2020].
VI. A. Ouda, “Development of high-performance heavy density concrete using different aggregates for gamma-ray shielding”, Progress in Nuclear Energy, vol. 79, pp. 48-55, 2015. Available: 10.1016/j.pnucene.2014.11.009 [Accessed 8 October 2020].
VII. Pignatelli, A. Kumar, R. Alizadeh, Y. Le Pape, M. Bauchy and G. Sant, “A dissolution-precipitation mechanism is at the origin of concrete creep in moist environments”, The Journal of Chemical Physics, vol. 145, no. 5, p. 054701, 2016. Available: 10.1063/1.4955429 [Accessed 8 October 2020].
VIII. Pignatelli, A. Kumar, R. Alizadeh, Y. Le Pape, M. Bauchy and G. Sant, “A dissolution-precipitation mechanism is at the origin of concrete creep in moist environments”, The Journal of Chemical Physics, vol. 145, no. 5, p. 054701, 2016. Available: 10.1063/1.4955429 [Accessed 8 October 2020].
IX. .Rudnov, V. Belyakov and R. Galiakhmetov, “New Concrete for Protection from Radiation in the Urals Based on Natural Fillers”, Solid State Phenomena, vol. 284, pp. 1042-1046, 2018. Available: 10.4028/www.scientific.net/ssp.284.1042 [Accessed 8 October 2020].
X. Rudnov V., V. Belyakov and R. Galiakhmetov, “New Concrete for Protection from Radiation in the Urals Based on Natural Fillers”, Solid State Phenomena, vol. 284, pp. 1042-1046, 2018. Available: 10.4028/www.scientific.net/ssp.284.1042 [Accessed 8 October 2020].
XI. khan Imtiaz, Intikhab Ahmad, Fawad Ahmed, Muhammad Zeeshan Ahad, : Mechanical behavior of concrete having springs at different zones, J. Mech. Cont.& Math. Sci., Vol.-14, No.-3, May-June (2019) pp 385-392

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Journal Vol – 15 No -11, November 2020

BLACKSPOTS IDENTIFICATION AND ACCIDENT ANALYSIS OF INDUS HIGHWAY (N-55)

Authors:

Muhammad Majid Naeem, Fazle Subhan, Kashif Yaqub, Muhammad Ikhlas Khan, Junaid Ahmad, Muner Khan

DOI NO:

https://doi.org/10.26782/jmcms.2020.11.00015

December 1, 2020

Abstract:

Traffic accidents are unavoidable in human life therefore highway safety is one of the most important factors of transportation engineering. After the advent of National highways and freeways, developing nations including Pakistan is facing new dimensions of highway safety challenges, highway safety management demands more attention due to the involvement of high-speed dynamics. This study presents a method by which accident-prone locations commonly termed as Blackspots are been identified. A stretch of 188 KM of National Highway N-55 also known as Indus highway from Peshawar to Lakki Marwat has been selected for the study. Road traffic accident data was only available with local district police in a manual file record (First Investigation Report). Accident data were collected from nine police stations along the selected route for seven years i.e. from 2013 to 2019. After analysis, it was found that most of the accidents occurred due to over speeding and geometric problems. Moreover, it was also found that there are no proper pedestrian crossings. The data was analyzed month and year wise. Fourteen such locations on which five or more fatalities occurred were identified as blackspots.  The blackspots are within the range of 1KM.

Keywords:

Transportation engineering,High-speed dynamics,Accident analysis,Blackspots,

Refference:

I. Adeed Khan, Asif Subhan, Muhammad Hasnain, Mohammad Adil, Muhammad Amar Rafiq, 6Mehre Munir, : Identification of Risk Management in Bus Rapid Transit (BRT) Project Peshawar, J.Mech.Cont.& Math. Sci., Vol.-14, No.2, March-April (2019) pp 87-99
II. Aziz Kamran , Kamran Ahmad , S.M. Tariq Shah, : TRUCK LOADING PATTERN AND ITS IMPACT ON PAVEMENT DESIGN, J. Mech. Cont.& Math. Sci., Vol.-15, No.-3, March (2020) pp 238-25.
III. Daud, N., and Ibrahim, K. (2007). “Ranking Accident Blackspots with reference to cost of accident using Hierarchical Bayesian Approach.” International journal of Energy and Environment, 1(2).

IV. Elvik, R. (2008). “State of the Art Approaches to Black Spot Management and Highway Safety Analysis for road Networks.” The Institute of Transport Economics (TOI) 883.

V. Hafeez, I., and Kamal,M.(2008). “Accidents Black Spots on Highways and Their Low Cost Remedial Measures”, Proceedings of Fourteenth International Conference on Urban Transport and the Environment in the 21st Century, 1 – 3 September 2008, Malta.

VI. Kockelman, K., and Ma, J.(2007). “Freeways speed and speed Variations Proceeding Accidents, within and Across Lanes.” Journal of the transportation Research 46(1) 43-62.

VII. Meuleners, L. B., Hendrie, D., Lee, A. H., and Legge, M. (2008). “Effectiveness of the Black Spot Programs in Western Australia.” Accident Analysis & Prevention, 40(3), 1211- 1216.

VIII. Milton, J. C., Shankar, V. N., and Mannering, F. L. (2008). “Highway accident severities and the mixed logit model: An exploratory empirical analysis.” Accident Analysis & Prevention, 40(1), 260-266.

IX. Mustakim, F., and Fujita, M. (2011). “Development of Accident Prediction Model for Rural Roadway.” World Academy of Science, 58.

X. National Transport Research Center (NTRC), (1985). “Road Accident Counter Measures in Pakistan.” National Transport Research Center NTRC-85.

XI. National Transport Research Center (NTRC), (1994). “Road Accident Investigation.” National Transport Research Center, NTRC-179.

XII. National Transport Research Center (NTRC), (1995). “Accident Black Spots Study on National Highway (N-5) Hassanabdal- Attock.” National Transport Research Center, NTRC-185.

XIII. Sims, A. G., Somenahalli, SVC (2010). “Hot Spot Identification using frequency of distinct crash types rather than total crashes.” Australasian Transport Research Forum.

XIV. Vadlamani, S., Chen, E., Ahn, S. And Washington, S.(2011) “Identifying large trucks Hotspots using crash counts and PODE’s.”Journal of transportation Engineering, 137(1).

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Journal Vol – 15 No -11, November 2020

ANALYSIS OF DRINKING WATER QUALITY OF PESHAWAR CITY

Authors:

Engr. Furqan wali, Muhammad Asim Khan Marwat, Usama Raheel, Abid Ullah, Engr. Marvan Raza

DOI NO:

https://doi.org/10.26782/jmcms.2020.11.00016

December 1, 2020

Abstract:

In this paper, the authors analyze the drinking water quality of Peshawar city due to which authors concluded that water quality assessment of 18 locations inside Peshawar of various union council. Groundwater samples were collected from a tube well and subjected to physical, chemical and biological analysis to check their suitability for the purpose of drinking. Results exposed that out of 18 samples 10 samples of water were found unfit for drinking purposes. In the 10, samples most of the effect on the water quality was from the chemical and biological contamination. It is concluded that the old defective supply system, infrastructure and storage, as well as their lack of maintenance are the reason behind the pollution of drinking water in Peshawar.

Keywords:

water quality assessment,physical,chemical and biological analysis,purpose of drinking Ground Water,Tube well,

Refference:

I. Ghulam Qadir Shar, Abdul Raheem Shar, Noor-Ul-Hassan Shar, Wahid Bux Jatoi, Waqas Mustafa Ghori at el in 2014 “Assessment of the quality of drinking water of Thari.

II. Mirwah Town and Surrounding Villages, District Khairpur, Sindh, Pakistan” where the Assessment of the Quality of Drinking water was done by Ghulam Qadir Shah in 2014.
III. M.K. Daud, Muhammad Nafees at el in 2017 “Drinking water quality status and contamination in Pakistan”.
IV. Muhammad Sheeraz, Muhammad Nadeem Khan, Muhammad Zeeshan Ahad, Fawad Ahmad, Mehr-e-Munir,: Effluents of Hayatabad Industrial Estate and Its Impacts on Human Health and Environment, J. Mech. Cont. & Math. Sci., Vol.-13, No.-5, November-December (2018) Pages 248-262
V. Shams Ali Baig, Zimo Lou, Muzaffar Ali Baig, Muhammad Qassim, Dilawar Farhan Shams, Qaisar Mahmood and Xinhua Xu at el in 2017 “Assessment of tap water quality and corrosion scales from the selected distribution systems in northern Pakistan”.
VI. Shams Ali Baig, Qaisar Mahmood, Bahadar Nawab, Mustafa Nawaz Shafqat, Arshid Pervez at el, 2017 “improvement of drinking water quality by using plant biomass through household biosand filter – A decentralized approach”.
VII. Sara Shoaib Khan, Huma Tareen, Uzma Jabeen, Fariha Mangal, Zubia Masood, Sana Ahmed, Sherino Bibi, Musarat Riaz, Sabena Rizwan, Fazila Mandokhail, Uzma Irum, and Rabia Mangal in 2015 “Quality assessment of drinking water from the different colonies of Quetta city, Pakistan according to WHO Standards”.
VIII. Sardar khan, Rabia Rauf at el in 2014 2017 “Arsenic and heavy metals health risk assessment through drinking water consumption in the Peshawar District, Pakistan”.
IX. Toqeer Ahmad, Saba Imdad and Noor Mohammad Butt at el, in 2014 “Bacteriological assessment of drinking water of Islamabad Capital Territory, Pakistan”.
X. Z. A. Soomro, Dr. M. I. A. Khokhar, W. Hussain and M. Hussain at el in 2011 “Drinking water quality challenges in Pakistan”.

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Journal Vol – 15 No -11, November 2020

A COMPARATIVE EXPLORATION ON DIFFERENT NUMERICAL METHODS FOR SOLVING ORDINARY DIFFERENTIAL EQUATIONS

Authors:

Mohammad Asif Arefin, Biswajit Gain, Rezaul Karim, Saddam Hossain

DOI NO:

https://doi.org/10.26782/jmcms.2020.12.00001

December 28, 2020

Abstract:

In this paper, the initial value problem of Ordinary Differential Equations has been solved by using different Numerical Methods namely Euler’s method, Modified Euler method, and Runge-Kutta method. Here all of the three proposed methods have to be analyzed to determine the accuracy level of each method. By using MATLAB Programming language first we find out the approximate numerical solution of some ordinary differential equations and then to determine the accuracy level of the proposed methods we compare all these solutions with the exact solution. It is observed that numerical solutions are in good agreement with the exact solutions and numerical solutions become more accurate when taken step sizes are very much small. Lastly, the error of each proposed method is determined and represents them graphically which reveals the superiority among all the three methods. We fund that, among the proposed methods Runge-Kutta 4th order method gives the accurate result and minimum amount of error.

Keywords:

Initial Value Problems (IVP),Euler’s Method,Modified Euler Method,Fourth-order Runge-Kutta Method,Error Estimation,

Refference:

I. Akanbi, M. A. (2010). Propagation of Errors in Euler Method, Scholars Research Library. Archives of Applied Science Research, 2, 457-469.

II. Hahn, G. D. (1991). A modified Euler method for dynamic analyses. International Journal for Numerical Methods in Engineering, 32(5), 943-955.

III. Hamed, A. B., Yuosif, I., Alrhaman, I. A., & Sani, I. (2017). The accuracy of Euler and modified Euler technique for first order ordinary differential equations with initial condition. Am. J. Eng. Res., 6, 334-338.

IV. Hong-Yi, L. (2000). The calculation of global error for initial value problem of ordinary differential equations. International journal of computer mathematics, 74(2), 237-245.

V. Hossain, M. B., Hossain, M. J., Miah, M. M., & Alam, M. S. (2017). A comparative study on fourth order and butcher’s fifth order runge-kutta methods with third order initial value problem (IVP). Applied and Computational Mathematics, 6(6), 243-253.

VI. Hossain, M. J., Alam, M. S., & Hossain, M. B. (2017). A study on the Numerical Solutions of Second Order Initial Value Problems (IVP) for Ordinary Differential Equations with Fourth Order and Butcher’s Fifth Order Runge-Kutta Mthods. American Journal of Computational and Applied Mathematics, 7(5), 129-137.

VII. Islam, M. A. (2015). Accuracy Analysis of Numerical solutions of initial value problems (IVP) for ordinary differential equations (ODE). IOSR Journal of Mathematics, 11(3), 18-23.

VIII. Islam, M. A. (2015). Accurate solutions of initial value problems for ordinary differential equations with the fourth order Runge Kutta method. Journal of Mathematics Research, 7(3), 41.

IX. Islam, M. A. (2015). A Comparative Study on Numerical Solutions of Initial Value Problems (IVP) for Ordinary Differential Equations (ODE) with Euler and Runge Kutta Methods. American Journal of Computational Mathematics, 5(03), 393.

X. Kockler, N. (1994). Numerical Method for Ordinary Systems of Initial Value Problems.

XI. Lambert, J. D. (1973). Computational methods in ordinary differential equations.

XII. Mathews, J.H. (2005) Numerical Methods for Mathematics, Science and Engineering. Prentice-Hall, India. [9]

XIII. Ntouyas, S. K., & Tsamatos, P. C. (1997). Global existence for semilinear evolution integrodifferential equations with delay and nonlocal conditions. Applicable Analysis, 64(1-2), 99-105.

XIV. Ogunrinde, R. B., Fadugba, S. E., & Okunlola, J. T. (2012). On some numerical methods for solving initial value problems in ordinary differential equations. IOSR Journal of Mathematics, 1(3), 25-31.

XV. Samsudin, N., Yusop, N. M. M., Fahmy, S., & binti Mokhtar, A. S. N. (2018). Cube Arithmetic: Improving Euler Method for Ordinary Differential Equation Using Cube Mean. Indonesian Journal of Electrical Engineering and Computer Science, 11(3), 1109-1113.

XVI. Shampine, L. F., & Watts, H. A. (1971). Comparing error estimators for Runge-Kutta methods. Mathematics of computation, 25(115), 445-455.

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Journal Vol – 15 No -12, December 2020

SYNERGISTIC EFFECT OF SUGARCANE BAGASSE ASH AND MARBLE SLUDGE POWDER AS A PARTIAL REPLACEMENT OF CEMENT IN CONCRETE

Authors:

Zeeshan Ullah, Khan Shahzada, Syed Azmat Ali Shah, Nauman Wahab, Sajjad Wali Khan, Akhtar Gul, Samiullah Qazi, Malik Hammad Naseer

DOI NO:

https://doi.org/10.26782/jmcms.2020.12.00002

December 28, 2020

Abstract:

Marble sludge powder is produced as a by-product during the cutting and polishing of marble. Similarly, sugarcane bagasse ash is produced during the burning operation of sugarcane bagasse. Improper disposal of these waste materials poses a severe threat to the environment. The objective of this research study was to partially substitute cement with a binary mixture of SBA and MSP to reduce the environmental and health issues by adequately utilizing the waste material in the production of low-cost and eco-friendly concrete. For this purpose, a total of 174 concrete cylinders were tested. Apart from this, XRF and EDX tests were performed to determine the chemical composition of waste. Ordinary Portland cement was replaced with a binary mix of SBA and MSP from 0 to 40% by weight to achieve the synergistic effect. Various tests were performed, including compressive and splitting tensile strength and material tests, i.e. specific gravity, absorption capacity, sieve analysis, dry rodded unit weight, and moisture content. The tested specimens were compared with the control samples. The results showed that the difference between compressive and tensile strength up to 15% replacement is within targeted strength and slump. The optimized sample by partial substitution with a negligible effect on properties of concrete was SB10-MP5 and SB5-MP10. The increase in partial replacement above 15% will lead to a decrease in compressive and tensile strength. The cost per cubic meter of concrete was reduced by 8% as per MRS2019.

Keywords:

Sugarcane bagasse ash,marble sludge powder,EDX,XRF,

Refference:

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Journal Vol – 15 No -12, December 2020

EVALUATE THE INFLUENCE OF STEEL FIBERS ON THE STRENGTH OF CONCRETE USING PLASTIC WASTE AS FINE AGGREGATES

Authors:

Samiullah Qazi, , Attaul Haq, Sajjad Wali Khan, Fasih Ahmad Khan, Rana Faisal Tufail

DOI NO:

https://doi.org/10.26782/jmcms.2020.12.00003

December 28, 2020

Abstract:

The plastic existence in abundance and its low biodegradability affect the environment. In recent years, researchers have tested numerous recycling techniques. However, each has its demerits. One such technique is recycling plastic as aggregates in concrete. It improves the concrete thermal insulation but depreciates its compressive and tensile strength, which is its core property in the construction industry. The objective of this research work is to efficiently utilize the plastic aggregate in concrete without deteriorating its strength with the use of steel fibers. In total eight concrete mix configurations were studied in this research. The result discussion includes compressive strength, split tensile test, and toughness index. The steel fiber used in the concrete mix with recycled plastic as fine aggregates improved the concrete strength. Its effects increase with an increase in % vol replacement of plastic aggregates with fine aggregates from 5 to 20.

Keywords:

Concrete,compressive strength,tensile strength,recycled plastic granules,steel fibers,

Refference:

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Journal Vol – 15 No -12, December 2020

SOME RESULTS RELATED TO CONVEXIFIABLE FUNCTIONS

Authors:

Faraz Mehmood, , Asif R. Khan, M. Azeem Ullah Siddique

DOI NO:

https://doi.org/10.26782/jmcms.2020.12.00004

December 28, 2020

Abstract:

The present article is devoted to the class of convexifiable functions and related results. In this way, we would recapture the result of authors L. Maligranda et. al. and we would obtain new majorization type results for weighted convexifiable function. This article also recaptures similar results for convex function as well as for concave function

Keywords:

Convex Function,Convexifiable Function,Majorization,Karamata’s inequality,

Refference:

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IV. Asif R. Khan, Faraz Mehmood, Faisal Nawaz and Aamna Nazir, Some Remarks on Results Related to ∇−Convex Function, J. Math. Fund. Sci., to appear.
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Journal Vol – 15 No -12, December 2020

INVESTIGATION OF CLIMATE CHANGE VARIABILITY UNDER CLIMATE CHANGE CONDITIONS OVER THE SEMI-ARID REGION

Authors:

Hareef Ahmed Keerio, Sallahuddin Panhwar, Sabab Ali Shah, Abdul Muntaqim Naji, Asim Ali, Adnan Aftab

DOI NO:

https://doi.org/10.26782/jmcms.2020.12.00005

December 28, 2020

Abstract:

The purpose of the study was to investigate the variation in climatic parameters and possible climate effects in the Hyderabad region. The least-square regression method was used to find a linear change in climatic parameters (Temperature and Precipitation). The maximum, minimum, and mean temperatures; annual, and monsoon precipitations were considered under the study. In the last 100 years, the global temperature has been increased by 0.6 or 0.74 0C. In Hyderabad city, we predicted that the minimum temperature (Tmin), maximum temperature (Tmax), and mean temperature (Tmean) are varied in the range of 0.00490C/year to -0.01330C/year. The variability in the precipitation was observed in the last 30 years. Yearly and monsoon precipitation was decreasing with the rate of 1.24mm/year, and 1.34mm/year. The maximum precipitation occurs in July, August, and September; in the rest of the months, no or little precipitation occurred which may lead to a shortage of fresh water. 

Keywords:

Meteorology,Climate change variance,Least Square Regression analysis,Hyderabad region,Temperature and precipitation variance ,

Refference:

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Journal Vol – 15 No -12, December 2020