Archive

Abstract:

Right now, investigations are rigorously carried out on modeling the dynamic progress of (Covid-19) pandemic around the globe. Here we introduce a simple mathematical model for analyzing the dynamics of the Covid-19, considering only the number of cumulative cases. In the present work, the 5PL function is applied to study the Covid-19 spread in Iceland. The cumulative number of infected persons C(t) has been accurately fitted with the 5PL equation, giving rise to different epidemiological parameters. The result of the current examination reveals the effectiveness and efficacy of the 5PL function for exploring the Covid 19 dynamics in Iceland. The mathematical model is simple enough such that practitioners knowing algebra and non-linear regression analysis can employ it to examining the pandemic situation in different countries.

Keywords:

5PL Function,Covid-19 Pandemic,Daily Growth Rate,Iceland,Simulation,Tipping Point,

Refference:

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III. Asish Mitra, “Modified SIRD Model of Epidemic Disease Dynamics: A case Study of the COVID-19 Coronavirus,” J. Mech.Cont. & Math. Sci., Vol.-16, No.-2, February (2021) pp 1-8. DOI : 10.26782/jmcms.2021.02.00001
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VIII. Chowell, G., Hincapie-Palacio, D, Ospina, J, Pell, B, Tariq, A, Dahal, S, Moghadas, S, Smirnova, A, Simonsen, L, Viboud, C, “Using phenomenological models to characterize transmissibility and forecast patterns and final Burden of Zika epidemics,” PLoS Curr. (2016). https://doi.org/10.1371/currents.outbreaks.f14b2217c902f453d9320a43a35b9583.
IX. Chowell, G, “Fitting dynamic models to epidemic outbreaks with quantified uncertainty: a primer for parameter uncertainty, identifiability, and forecasts,” Infect. Dis. Model. 2(3), 379–398 (2017). https://doi.org/10.1016/j.idm.2017.08.001.
X. Chowell, G, Tariq, A, Hyman, J M, “A novel sub-epidemic modeling framework for short-term forecasting epidemic waves,” BMC Med. 17(1), 1–18 (2019). https://doi.org/10.1186/s12916-019-1406-6.
XI. Chowell, G, Luo, R, Sun, K, Roosa, K, Tariq, A, Viboud, C, “Real-time forecasting of epidemic trajectories using computational dynamic ensembles,” Epidemics. 30, 100379 (2020). https://doi.org/10.1016/j.epidem.2019.100379.

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XIV. Hsieh Y H, Lee J Y, Chang H L, “SARS epidemiology modeling. Emerging infectious diseases,” 2004; 10(6):1165. https://doi.org/10.3201/eid1006.031023 PMID: 15224675.
XV. Hsieh Y H, “Richards model: a simple procedure for real-time prediction of outbreak severity. In: Modelingand dynamics of infectious diseases,” World Scientific; 2009. p. 216–236. https://doi.org/10.1142/9789814261265_0009.
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XXVII. Wu K, Darcet D, Wang Q, Sornette D, “Generalized logistic growth modeling of the COVID-19 outbreak in 29 provinces in China and in the rest of the world,” arXiv preprint arXiv:200305681. 2020.
XXVIII. Viboud, C, Simonsen, L, Chowell, G, “A generalized growth model to characterize the early ascending phase of infectious disease outbreaks,” Epidemics 15, 27–37 (2016). https://doi.org/10.1016/j.epidem.2016.01.002.

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Abstract:

In this article, an iterative, bracketing and derivative-free method have been proposed with the second-order of convergence for the solution of non-linear equations. The proposed method derives from the Stirling interpolation technique, Stirling interpolation technique is the process of using points with known values or sample points to estimate values at unknown points or polynomials. All types of problems (taken from literature) have been tested by the proposed method and compared with existing methods (regula falsi method, secant method and newton raphson method) and it’s noted that the proposed method is more rapidly converges as compared to all other existing methods. All problems were solved by using MATLAB Version: 8.3.0.532 (R2014a) on my personal computer with specification Intel(R) Core (TM) i3-4010U CPU @ 1.70GHz with RAM 4.00GB and Operating System: Microsoft Windows 10 Enterprise Version 10.0, 64-Bit Server, x64-based processor.

Keywords:

Non-linear equation,Stirling Interpolation Technique,convergence,number of iterations,Accuracy,

Refference:

I. Ali Sial, A. et al. (2017) “Modified Algorithm for Solving Nonlinear Equations in Single Variable,” J. Appl. Environ. Biol. Sci, 7(5), pp. 166–171. Available at: www.textroad.com.
II. Allame, M. and Azad, N. (2012) “On Modified Newton Method for Solving a Nonlinear Algebraic Equations by Mid-Point,” World Applied Sciences Journal, 17(12), pp. 1546–1548.
III. Almomani, M. H., Alrefaei, M. H. and Mansour, S. Al (2018) “A method for selecting the best performance systems,” International Journal of Pure and Applied Mathematics, 120(September), pp. 191–202. doi: 10.12732/ijpam.v120i2.3.
IV. Bahgat, M. S. M. and Hafiz, M. A. (2012) “An Efficient Two-step Iterative Method for Solving System of Nonlinear Equations,” Journal of Mathematics Research, 4(4). doi: 10.5539/jmr.v4n4p28.
V. Sanaullah Jamali, Zubair Ahmed Kalhoro, Abdul Wasim Shaikh, Muhammad Saleem Chandio., : ‘A NEW SECOND ORDER DERIVATIVE FREE METHOD FOR NUMERICAL SOLUTION OF NON-LINEAR ALGEBRAIC AND TRANSCENDENTAL EQUATIONS USING INTERPOLATION TECHNIQUE’. J. Mech. Cont. & Math. Sci., Vol.-16, No.-4, April (2021) pp 75-84. DOI : 10.26782/jmcms.2021.04.00006.

VI. Kang, S. M. et al. (2015) “Improvements in Newton-Rapshon method for nonlinear equations using modified adomian decomposition method,” International Journal of Mathematical Analysis, pp. 1919–1928. doi: 10.12988/ijma.2015.54124.
VII. Khalid Qureshi, U. and Ahmed Kalhoro, Z. (2018) “NUMERICAL METHOD OF MODIFIED NEWTON RAPHSON METHOD WITHOUT SECOND DERIVATIVE FOR SOLVING THE NONLINEAR EQUATIONS,” Gomal University Journal of Research, 34(1).
VIII. Mir Md. Moheuddin, Uddin, M. J. and Md. Kowsher (2019) “A New Study To Find Out The Best Computational Method For Solving The Nonlinear Equation,” Applied Mathematics and Sciences An International Journal (MathSJ), 6(3), pp. 15–31. doi: 10.5121/mathsj.2019.6302.
IX. Omran, H. H. (2013) Modified Third Order Iterative Method for Solving Nonlinear Equations, Journal of Al-Nahrain University.
X. Qureshi, U. K. et al. (2020) “Sixth Order Numerical Iterated Method of Open Methods for Solving Nonlinear Applications Problems,” Proceedings of the Pakistan Academy of Sciences: A. Physical and Computational Sciences, 57(November), pp. 35–40.
XI. Qureshi, U. K., Jamali, S. and Kalhoro, Z. A. (2021) ‘MODIFIED QUADRATURE ITERATED METHODS OF BOOLE RULE AND WEDDLE RULE FOR SOLVING NON-LINEAR EQUATIONS’. J. Mech. Cont. & Math. Sci., Vol.-16, No.-2, February (2021) pp 87-101. DOI : 10.26782/jmcms.2021.02.00008
XII. Saeed Ahmed, M. et al. (2015) “NEW FIXED POINT ITERATIVE METHOD FOR SOLVING NONLINEAR FUNCTIONAL EQUATIONS,” Applied Mathematics, 27(3), pp. 1815–1817. doi: 10.4236/am.2015.611163.
XIII. Suhadolnik, A. (2012) “Combined bracketing methods for solving nonlinear
equations,” Applied Mathematics Letters, 25(11), pp. 1755–1760. doi:
10.1016/j.aml.2012.02.006.
XIV. Suhadolnik, A. (2013) “Superlinear bracketing method for solving nonlinear equations,” Applied Mathematics and Computation, 219(14), pp. 7369–7376. doi: 10.1016/j.amc.2012.12.064.

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Abstract:

The present study aims to analyze the structural behavior of the Darrieus Hydro-kinetic turbine at different upstream velocity values and rotational rates. For that purpose, one-way fluid-structure interaction is performed to predict stresses, deformation and fatigue life of the turbine. To determine real-time fluid loads three-dimensional fluid flow simulations were performed, the obtained fluid loads were transferred to the structural finite element analysis model. CFD simulation results were validated with experimental results from literature where the close agreement was noticed. Structural analysis results revealed that the highest stresses are produced in the struts and at the joint where the shaft is connected with struts. Moreover, it was also found that the stress produced in the turbine is highly non-linear against Tip Speed Ratio (TSR) i.e inflow water velocity. Finite Element Analysis (FEA) results showed that maximum values of stresses were found in the turbine strut having a value 131.99MPa, which lower than the yield strength of the material, the fatigue life of 117520 cycles and factor of safety 1.89. The study also found that increased inflow velocity results increase in stress and deformation produced in the turbine. Additionally, the study assumed Aluminum Alloy as turbine blade material, further; it was found that the blade which confronts flow, experience higher stresses. Moreover, the study concluded that strut, blade-strut joint and strut-shaft joint are the critical parts of the turbine, require careful design consideration. Furthermore, the study also suggests that the turbine blade may be kept hollow to reduce turbine weight; hence inertia and turbine struts and shaft should be made of steel or the material having higher stiffness and strength.

Keywords:

Structural loading,Hydrokinetic turbine,Turbine stress analysis,deflection,fatigue life,Factor of safety,

Refference:

I. Alia, I., et al. (2016). “131. Parametric Study of Three Blade Vertical Axis Micro Hydro Turbines (VAMHT) by changing Blade Characteristics.”

II. Castelli, M. R., et al. (2010). Modeling strategy and numerical validation for a Darrieus vertical axis micro-wind turbine. ASME 2010 international mechanical engineering congress and exposition, Citeseer.

III. Danao, L. A., et al. (2013). The Performance of a Vertical Axis Wind Turbine in Fluctuating Wind-A Numerical Study. Proceedings of the World Congress on Engineering.

IV. Golecha, K., et al. (2011). “Influence of the deflector plate on the performance of modified Savonius water turbine.” Applied Energy 88(9): 3207-3217.

V. Gopinath, D. and C. V. Sushma (2015). “Design and optimization of four wheeler connecting rod using finite element analysis.” Materials Today: Proceedings 2(4-5): 2291-2299.
VI. Ganthia Bibhu Prasad, Subrat Kumar Barik, Byamakesh Nayak, : ‘TRANSIENT ANALYSIS OF GRID INTEGRATED STATOR VOLTAGE ORIENTED CONTROLLED TYPE-III DFIG DRIVEN WIND TURBINE ENERGY SYSTEM’. J. Mech. Cont.& Math. Sci., Vol.-15, No.-6, June (2020) pp 139-157.
VII. Hameed, M. S. and S. K. Afaq (2013). “Design and analysis of a straight bladed vertical axis wind turbine blade using analytical and numerical techniques.” Ocean Engineering 57: 248-255.

VIII. Huang, S.-R., et al. (2014). “Theoretical and conditional monitoring of a small three-bladed vertical-axis micro-hydro turbine.” Energy conversion and management 86: 727-734.

IX. Kamoji, M., et al. (2008). “Experimental investigations on single stage, two stage and three stage conventional Savonius rotor.” International journal of energy research 32(10): 877-895.

X. Kamoji, M., et al. (2009). “Performance tests on helical Savonius rotors.” Renewable Energy 34(3): 521-529.

XI. Kamoji, M., et al. (2009). “Experimental investigations on single stage modified Savonius rotor.” Applied Energy 86(7): 1064-1073.

XII. Khan, M., et al. (2009). “Hydrokinetic energy conversion systems and assessment of horizontal and vertical axis turbines for river and tidal applications: A technology status review.” Applied energy 86(10): 1823-1835.

XIII. Kirke, B. (2011). “Tests on ducted and bare helical and straight blade Darrieus hydrokinetic turbines.” Renewable Energy 36(11): 3013-3022.

XIV. Kumar, A., et al. (2014). “DynamicAnalysis of Bajaj Pulsar 150cc Connecting Rod Using ANSYS 14.0.” Asian Journal of Engineering and Applied Technology ISSN 3(2): 19-24.

XV. Kumar, D. and P. Bhingole (2015). “CFD based analysis of combined effect of cavitation and silt erosion on Kaplan turbine.” Materials Today: Proceedings 2(4-5): 2314-2322.

XVI. Li, Y. and S. M. Calisal (2010). “Three-dimensional effects and arm effects on modeling a vertical axis tidal current turbine.” Renewable energy 35(10): 2325-2334.

XVII. Maître, T., et al. (2013). “Modeling of the flow in a Darrieus water turbine: Wall grid refinement analysis and comparison with experiments.” Renewable energy 51: 497-512.

XVIII. Malipeddi, A. and D. Chatterjee (2012). “Influence of duct geometry on the performance of Darrieus hydroturbine.” Renewable energy 43: 292-300.

XIX. Marsh, P., et al. (2012). Three dimensional numerical simulations of a straight-bladed vertical axis tidal turbine. 18th Australasian fluid mechanics conference.

XX. Marsh, P., et al. (2016). “Numerical simulation of the loading characteristics of straight and helical-bladed vertical axis tidal turbines.” Renewable energy 94: 418-428.

XXI. Marsh, P., et al. (2017). “The influence of turbulence model and two and three-dimensional domain selection on the simulated performance characteristics of vertical axis tidal turbines.” Renewable energy 105: 106-116.

XXII. Marsh, P. J. (2015). The hydrodynamic and structural loading characteristics of straight and helical-bladed vertical axis tidal and current flow turbines, University of Tasmania.

XXIII. Momčilović, D., et al. (2012). “Failure analysis of hydraulic turbine shaft.” Engineering failure analysis 20: 54-66.

XXIV. Nagendrababu Mahapatruni, Velangini Sarat P., Suresh Mallapu, Durga Syamprasad K., : ‘A SCIENTIFIC APPROACH TO CONTROL THE SPEED DEVIATION OF DUAL REGULATED LOW-HEAD HYDRO POWER PLANT CONNECTED TO SINGLE MACHINE INFINITE BUS’. J. Mech. Cont. & Math. Sci., Vol.-15, No.-8, August (2020) pp 136-150. DOI : 10.26782/jmcms.2020.08.00013

XXV. Paraschivoiu, I. and N. V. Dy (2012). A numerical study of darrieus water turbine. The Twenty-second International Offshore and Polar Engineering Conference, International Society of Offshore and Polar Engineers.

XXVI. Patel, V., et al. (2017). “Experimental investigations on Darrieus straight blade turbine for tidal current application and parametric optimization for hydro farm arrangement.” International journal of marine energy 17: 110-135.

XXVII. Saeed, R., et al. (2010). “Modelling of flow-induced stresses in a Francis turbine runner.” Advances in Engineering Software 41(12): 1245-1255.

XXVIII. Sangal, S., et al. (2013). “Review of optimal selection of turbines for hydroelectric projects.” International Journal of Emerging Technology and Advance Engineering 3: 424-430.

XXIX. Sarma, N., et al. (2014). “Experimental and computational evaluation of Savonius hydrokinetic turbine for low velocity condition with comparison to Savonius wind turbine at the same input power.” Energy Conversion and Management 83: 88-98.

XXX. Sick, M., et al. (2009). Recent developments in the dynamic analysis of water turbines, SAGE Publications Sage UK: London, England.

XXXI. Tsai, J.-S. and F. Chen (2014). “The conceptual design of a tidal power plant in Taiwan.” Journal of Marine Science and Engineering 2(2): 506-533.

XXXII. Tunio, I. A., et al. (2020). “Investigation of duct augmented system effect on the overall performance of straight blade Darrieus hydrokinetic turbine.” Renewable Energy 153: 143-154.

XXXIII. Xiao, R., et al. (2008). “Dynamic stresses in a Francis turbine runner based on fluid-structure interaction analysis.” Tsinghua Science & Technology 13(5): 587-592.

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Abstract:

There are various methods to solve the physical life problem involving engineering, scientific and biological systems. It is found that numerical methods are approximate solutions. In this way, randomly generated finite difference grids achieve an approximation with fewer iterations. The idea of randomly generated grids in cartesian coordinates and polar form are compared with the exact, iterative method, uniform grids, and approximate solutions in a generalized expansion form of two-dimensional fractional-order Legendre functions. The most ideal and benchmarking method is the finite difference method over randomly generated grids on Cartesian coordinates, polar coordinates used for numerical solutions. This concept motivates the investigation of the effects of the randomly generated meshes. The two-dimensional equation is solved over randomly generated meshes to test randomly generated grids and the implementation. The feasibility of the numerical solution is analyzed by comparing simulation profiles.

Keywords:

Partial differential equation,Finite difference method,Polar coordinates,Randomly generated grids,Uniform meshes,fractional-order Legendre functions,

Refference:

I. A. Mahmood, M.F. Md Basir, U. Ali, M.S. Mohd Kasihmuddin, andM. Mansor, Numerical solutions of heat transfer for magneto hydrodynamic jeffery-hamel flow using spectral Homotopy analysis method. Processes 7 (2019) 626.
II. A.-R. Khaled, Modeling and computation of heat transfer through permeable hollow-pin systems. Advances in Mechanical Engineering 4 (2012) 587165.
III. A.E. Abouelregal, M.V. Moustapha, T.A. Nofal, S. Rashid, andH. Ahmad, Generalized thermoelasticity based on higher-order memory-dependent derivative with time delay. Results in Physics 20 (2021) 103705.
IV. C.S.E.T.O.S. Natarajan, A review of the scaled boundary finite element method for two-dimensional linear elastic fracture mechanics. Engineering Fracture Mechanics 187 (2018) 43.
V. C. Song, E.T. Ooi, andS. Natarajan, A review of the scaled boundary finite element method for two-dimensional linear elastic fracture mechanics. Engineering Fracture Mechanics 187 (2018) 45-73.
VI. D.S. Lubinsky, and I.E. Pritsker, Variance of real zeros of random orthogonal polynomials. Journal of Mathematical Analysis and Applications 498 (2021) 124954.
VII E. Samaniego, C. Anitescu, S. Goswami, V.M. Nguyen-Thanh, H. Guo, K. Hamdia, X. Zhuang, and T. Rabczuk, An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications. Computer Methods in Applied Mechanics and Engineering 362 (2020) 112790.

VIII. G.B. Folland, Introduction to partial differential equations, Princeton university press, 2020.
IX H. Meng, F.-S. Lien, E. Yee, andJ. Shen, Modelling of anisotropic beam for rotating composite wind turbine blade by using finite-difference time-domain (FDTD) method. Renewable Energy 162 (2020) 2361-2379.
X. H. Ahmad, Auxiliary parameter in the variational iteration algorithm-II and its optimal determination. Nonlinear Sci. Lett. A 9 (2018) 62-72.
XI. H. Ahmad, Variational iteration method with an auxiliary parameter for solving differential equations of the fifth order. Nonlinear Sci. Lett. A 9 (2018) 27-35.
XII. H. Ahmad, A.R. Seadawy, T.A. Khan, andP. Thounthong, Analytic approximate solutions for some nonlinear Parabolic dynamical wave equations. Journal of Taibah University for Science 14 (2020) 346-358.
XIII. H. Wang, and N. Yamamoto, Using a partial differential equation with Google Mobility data to predict COVID-19 in Arizona. Mathematical Biosciences and Engineering 17 (2020).
XIV. J.W. Thomas, Numerical partial differential equations: finite difference methods, Springer Science & Business Media, 2013.
XV. J.H. He, and Y.O. El‐Dib, The reducing rank method to solve third‐order Duffing equation with the homotopy perturbation. Numerical Methods for Partial Differential Equations 37 (2021) 1800-1808.
XVI. J. Andreasen, and B.N. Huge, Finite difference based calibration and simulation. Available at SSRN 1697545 (2010).
XVII. K.S. Miller, Partial differential equations in engineering problems, Courier Dover Publications, 2020.
XVIII. M. Bibi, Y. Nawaz, M.S. Arif, J.N. Abbasi, U. Javed, andA. Nazeer, A Finite Difference Method and Effective Modification of Gradient Descent Optimization Algorithm for MHD Fluid Flow Over a Linearly Stretching Surface. Computers, Materials & Continua 62 (2020) 657-677.
XIX. Q. Liu, F. Liu, I. Turner, andV. Anh, Approximation of the Lévy–Feller advection–dispersion process by random walk and finite difference method. Journal of Computational Physics 222 (2007) 57-70.
XX. Rafiuddin, Noushima Humera. G., : NUMERICAL SOLUTION OF UNSTEADY, : TWO DIMENSIONAL HYDROMAGNETICS FLOW WITH HEAT AND MASS TRANSFER OF CASSON FLUID. J. Mech. Cont.& Math. Sci., Vol.-15, No.-9, September (2020) pp 17-30. DOI: 10.26782/jmcms.2020.09.00002
XI. S. Mastoi, A.B. Mugheri, N.B. Kalhoro, andA.S. Buller, Numerical solution of Partial differential equations(PDE’s) for nonlinear Local Fractional PDE’s and Randomly generated grids. International Journal of Disaster Recovery and Business Continuity 11 (2020) 2429-2436.
XXII. S. Mastoi, N.B. Kalhoro, A.B.M. Mugheri, U.A. Rajput, R.B. Mastoi, N. Mastoi, and W.A.M. Othman, Numerical solution of Partial differential equation using finite random grids. International Journal of Advanced Research in Engineering and Technology (IJARET) (2021).
XXIII. S. Yao, W. Gu, C. Zhu, S. Zhou, Z. Wu, andZ. Zhang, A Novel Cross Iteration Method for Dynamic Energy Flow Calculation of the Hot-water Heating Network in the Integrated Energy System, 2020 IEEE 4th Conference on Energy Internet and Energy System Integration (EI2), IEEE, pp. 23-28.
XXIV. S. Mastoi, and W.A.M. Othman, A Finite difference method using randomly generated grids as non-uniform meshes to solve the partial differential equation. International Journal of Disaster Recovery and Business Continuity 11 (2020) 1766-1778.
XXV. S. Mastoi, N.B. Kalhoro, A.B. Mugheri, A.S. Buller, U.A. Rajput, R.B. Mastoi, andN. Mastoi, A Statistical analysis for Mathematics & Statistics in Engineering Technologies (Random Sampling). International Journal of Management 12 (2021) 416-421.
XXVI. S. Mastoi, A.B.M. Mugheri, N.B. Kalhoro, U.A. Rajput, R.B. Mastoi, N. Mastoi, andW.A.M. Othman, Finite difference algorithm on Finite random grids. International Journal of Advanced Research in Engineering and Technology (IJARET) (2021).
XXVII. S. Mastoi, W.A.M. Othman, andK. Nallasamy., Numerical Solution of Second order Fractional PDE’s by using Finite difference Method over randomly generated grids. International Journal of Advance Science and Technology 29 (2020) 373-381.
XXVIII. S. Mastoi, W.A.M. Othman, andK. Nallasamy., Randomly generated grids and Laplace Transform for Partial differential equation. International Journal Disaster Recovery and Business continuity 11 (2020) 1694-1702.
XXIX. S.J. Shyu, Image encryption by random grids. Pattern Recognition 40 (2007) 18.
XXX. S.-T. Saeed, M.-B. Riaz, D. Baleanu, A. Akgül, andS.-M. Husnine, Exact Analysis of Second Grade Fluid with Generalized Boundary Conditions. Intelligent Automation & Soft Computing 28 (2021) 547–559.
XXXI. T. Bonnafont, R. Douvenot, andA. Chabory, A local split‐step wavelet method for the long range propagation simulation in 2D. Radio Science 56 (2021) e2020RS007114.
XXXII. T.A.V.V.S.S.P.M.S.S. Dinesh., Potential Flow Simulation through Lagrangian Interpolation Meshless Method Coding. Journal of Applied Fluid Mechanics 11 (2018) 7.
XXXIII. U. Ali, M. Sohail, andF.A. Abdullah, An efficient numerical scheme for variable-order fractional sub-diffusion equation. Symmetry 12 (2020) 1437.
XXXIV. U. Rashid, H. Liang, H. Ahmad, M. Abbas, A. Iqbal, andY. Hamed, Study of (Ag and TiO2)/water nanoparticles shape effect on heat transfer and hybrid nanofluid flow toward stretching shrinking horizontal cylinder. Results in Physics 21 (2021) 103812.
XXXV. W. Cao, W. Huang, andR.D. Russell, Anr-adaptive finite element method based upon moving mesh PDEs. Journal of Computational physics 149 (1999) 221-244.
XXXVI. Y. Sun, W. Sun, andH. Zheng, Domain decomposition method for the fully-mixed Stokes–Darcy coupled problem. Computer Methods in Applied Mechanics and Engineering 374 (2021) 113578.
XXXVII. Y. Bar-Sinai, S. Hoyer, J. Hickey, andM.P. Brenner, Learning data-driven discretizations for partial differential equations. Proc Natl Acad Sci U S A 116 (2019) 15344-15349.
XXXVIII. Y. Gu, L. Wang, W. Chen, C. Zhang, andX. He, Application of the meshless generalized finite difference method to inverse heat source problems. International Journal of Heat and Mass Transfer 108 (2017) 721-729.

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Abstract:

Fuzzy sets (FSs) are an important tool to model uncertainty and vagueness. Entropy is being used to measure the fuzziness within a fuzzy set (FS). These entropies are used to find multicriteria decision-making. For measuring uncertainty with TOPSIS techniques an axiomatic definition of entropy measure for fuzzy sets is also given in this paper. The proposed entropy is provided to satisfy all the axioms. Several numerical examples are presented to compare the proposed entropy measure with existing entropies. The corresponding results show that the newly proposed entropy can be computed easily and give reliable results. Finally, the decision-making algorithm TOPSIS (Techniques of ordered preference similarity to ideal solution) is utilized to solve multicriteria decision-making problems (MCDM) related to daily life.  In the current situation, COVID-19 has no proper medical treatment. We use TOPSIS technique to suggest an effective medicine for this pandemic. Numerical results and practical examples show the effectiveness and practical applicability of the proposed entropy.

Keywords:

Fuzzy entropy,TOPSIS,Uncertainty,Multicriteria Decision Making,

Refference:

I. Asish Mitra, : ‘MODIFIED SIRD MODEL OF EPIDEMIC DISEASE DYNAMICS: A CASE STUDY OF THE COVID-19 CORONAVIRUS’. J. Mech. Cont. & Math. Sci., Vol.-16, No.-2, February (2021) pp 1-8.
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XII. Hussain, Zahid, and Miin-Shen Yang. “Entropy for hesitant fuzzy sets based on Hausdorff metric with construction of hesitant fuzzy TOPSIS.” International Journal of Fuzzy Systems” 20, no. 8 (2018): 2517-2533.
XIII. H. wang, Chao-Ming, and Miin-Shen Yang. “On entropy of fuzzy sets.” International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 16, no. 04 (2008): 519-527.
XIV. Kosko, Bart. “Fuzzy entropy and conditioning.”Information sciences 40, no. 2 (1986): 165-174.
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XVI. Lee, Kwang Hyung. “First course on fuzzy theory and applications.” Springer Science & Business Media, 27 (2004).
XVII. Li, Pingke, and Baoding Liu. “Entropy of credibility distributions for fuzzy variables.” IEEE Transactions on Fuzzy Systems 16, no. 1 (2008): 123-129.
XVIII. Malone, David, and Wayne Sullivan. “Guesswork is not a substitute for entropy.” (2005): 1-5.
XIX. Pal, Nikhil R., and Sankar K. Pal. “Some properties of the exponential entropy.” Information sciences 66, no. 1-2 (1992): 119-137.
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Abstract:

The construction of divergence measures between two Pythagorean fuzzy sets (PFSs) is significant as it has a variety of applications in different areas such as multicriteria decision making, pattern recognition and image processing. The main purpose of this study to introduce an information-theoretic divergence so-called Pythagorean fuzzy Jensen-Rényi divergence (PFJRD) between two PFSs. The strength and characterization of the proposed Jensen-Rényi divergence between Pythagorean fuzzy sets lie in its practical applications which are very closed to real life. The proposed divergence measure is utilized to induce some useful similarity measures between PFSs. We apply them in pattern recognition, characterization of the similarity between linguistic variables and in multiple criteria decision making. To demonstrate the practical utility and applicability, we present some numerical examples related to daily life with the construction of Pythagorean fuzzy TOPSIS (Techniques of preference similar to ideal solution). Which is utilized to rank the Belt and Road initiative (BRI) projects. Our numerical simulation results show that the suggested measures are well suitable in pattern recognition, characterization of linguistic variables and multi-criteria decision-making environment.

Keywords:

Divergence measure,Intuitionistic fuzzy set (IFS),Pythagorean fuzzy set (PFS),Pattern recognition,similarity measure,multicriteria decision making,

Refference:

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IX. Candan, K. S., Li, W. S., & Priya, M. L. (2000). Similarity-based ranking and query processing in multimedia databases. Data & Knowledge Engineering, 35(3), 259-298.
X. Garg, H. (2016). A new generalized Pythagorean fuzzy information aggregation using Einstein operations and its application to decision making. International Journal of Intelligent Systems, 31(9), 886-920.
XI. Gou, X., Xu, Z., & Ren, P. (2016). The properties of continuous Pythagorean fuzzy information. International Journal of Intelligent Systems, 31(5), 401-424.
XII. Hussian, Z., & Yang, M. S. (2019). Distance and similarity measures of Pythagorean fuzzy sets based on the Hausdorff metric with application to fuzzy TOPSIS. International Journal of Intelligent Systems, 34(10), 2633-2654.
XIII. Hwang, C. M., & Yang, M. S. (2016). Belief and plausibility functions on intuitionistic fuzzy sets. International Journal of Intelligent Systems, 31(6), 556-568.
XIV. He, Y., Hamza, A. B., & Krim, H. (2003). A generalized divergence measure for robust image registration. IEEE Transactions on Signal Processing, 51(5), 1211-1220.
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XVI. Lin, J. (1991). Divergence measures based on the Shannon entropy. IEEE Transactions on Information theory, 37(1), 145-151.

XVII. Hwang, C. M., Yang, M. S., & Hung, W. L. (2018). New similarity measures of intuitionistic fuzzy sets based on the Jaccard index with its application to clustering. International Journal of Intelligent Systems, 33(8), 1672-1688.
XVIII. Mitchell, H. B. (2003). On the Dengfeng–Chuntian similarity measure and its application to pattern recognition. Pattern Recognition Letters, 24(16), 3101-3104.
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XXI. Peng, X., & Yang, Y. (2017). Algorithms for interval-valued fuzzy soft sets in stochastic multi-criteria decision making based on regret theory and prospect theory with combined weight. Applied Soft Computing, 54, 415-430.
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XXVI. R. Shashi Kumar Reddy, M.S. Teja, M. Sai Kumar, Shyamsunder Merugu, : ‘MATHEMATICAL INPUT-OUTPUT RELATIONSHIPS & ANALYSIS OF FUZZY PD CONTROLLERS’. J. Mech. Cont. & Math. Sci., Vol.-15, No.-8, August (2020) pp 330-340. DOI : 10.26782/jmcms.2020.08.00031
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Abstract:

Friction stir welding (FSW) has many advantages when compared with another fusion welding. The experimental analysis and optimization of friction stir welding (FSW) were done to obtain desired mechanical properties of dissimilar aluminum welded plates (2024T3 and 7075T6). The friction stir welding process was done on aluminum plates (2024T3 and 7075T6) for different three rotating speeds (710, 1120 and 1800), three welding speeds (25, 50 and 77), three different steel tools (Square, cylindrical and Hexagonal) and 2° title angle. The different tests of welding were done according to the orthogonal matrix of experimental design analysis, then a tensile test was done to calculate the ultimate stress to get the welding efficiency. The optimum welding environment led to the maximum efficiency was obtained by these methods (Taguchi, Particle Swarm Optimization and new modified Particle Swarm Optimization).  Particle swarm optimization (and its new modification) used an artificial neural network to find the relation between the input and output parameters. The results showed that when the rotating speed is increased and welding speed is decreased (but this conclusion depends on tool shape) the welding efficiency is increased. The present study showed that the modified PSO is the best method to find the optimum welding environment as compared with experimental results.

Keywords:

dissimilar aluminum plates,Particle Swarm Optimization,Taguchi,

Refference:

I. ASM Handbook, “Properties and Selection: Non-Ferrous Alloys and Special Purposes Materials”, American Society for Metals, Vol. 2, (1992).
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VII. Lam Suvarna Raju, Venu Borigorla, : ‘MULTI OBJECTIVE OPTIMIZATION OF FSW PROCESS PARAMETERS USING GENETIC ALGORITHM AND TLBO ALGORITHM’. J. Mech. Cont.& Math. Sci., Vol.-15, No.-7, July (2020) pp 480-494. DOI : 10.26782/jmcms.2020.07.00042
VIII. Masayuki Aonuma and Kazuhiro Nakata, “Dissimilar Metal Joining of 2024 and 7075 Aluminum Alloys to Titanium Alloys by Friction Stir Welding”, Materials Transactions, Vol. 52, No. 5 (2011) pp. 948 to 952.
IX. Murali Ambekar, Jayant Kittur, ” Multiresponse optimization of friction stir welding process parameters by an integrated WPCA-ANN-PSO approach”, Materials Today: Proceedings, First International Conference on Recent Advances in Materials and Manufacturing 2019.
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Abstract:

Finding the single root of nonlinear equations is a classical problem that arises in a practical application in Engineering, Physics, Chemistry, Biosciences, etc. For this purpose, this study traces the development of a novel numerical iterative method of an open method for solving nonlinear algebraic and transcendental application equations. The proposed numerical technique has been founded from Secant Method and Newton Raphson Method, and the proposed method is compared with the Modified Newton Method and Variant Newton Method. From the results, it is pragmatic that the developed numerical iterative method is improving iteration number and accuracy with the assessment of the existing cubic method for estimating a single root nonlinear application equation.

Keywords:

applications equations,cubic methods,open methods,convergence,results,

Refference:

I. Adnan Ali Mastoi , Muhammad Mujtaba Shaikh, Abdul Wasim Shaikh. ‘A NEW THIRD-ORDER DERIVATIVE-BASED ITERATIVE METHOD FOR NONLINEAR EQUATIONS’. J. Mech. Cont.& Math. Sci., Vol.-15, No.-10, October (2020) pp 110-123. DOI : 10.26782/jmcms.2020.10.00008
II. Akram, S. and Q. U. Ann., (2015), Newton Raphson Method, International Journal of Scientific & Engineering Research, Vol. 6.
III. Allame M., and N. Azad, (2012), On Modified Newton Method for Solving a Nonlinear Algebraic Equations by Mid-Point, World Applied Sciences Journal, Vol. 17(12), pp. 1546-1548, ISSN 1818-4952 IDOSI Publications.
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VIII. Kang, S. M., (2015), Improvements in Newton-Raphson Method for Non-linear Equations Using Modified Adomian Decomposition Method, International Journal of Mathematical Analysis Vol. 9.
IX. Qureshi, U. K., (2017), Modified Free Derivative Open Method for Solving Non-Linear Equations, Sindh University Research Journal, Vol.49(4), pp. 821-824.
X. Qureshi, U. K. and A. A. Shaikh, (2018), Modified Cubic Convergence Iterative Method for Estimating a Single Root of Nonlinear Equations, J. Basic. Appl. Sci. Res., Vol. 8(3) pp. 9-13.
XI. Rajput, k., A. A. Shaikh and S. Qureshi, “Comparison of Proposed and Existing Fourth Order Schemes for Solving Non-linear Equations, Asian Research Journal of Mathematics, Vol. 15, No. 2, pp.1-7, 2019.
XII. Sehrish Umar, 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. DOI : 10.26782/jmcms.2020.10.00006.
XIII. Singh, A. K., M. Kumar and A. Srivastava, (2015), A New Fifth Order Derivative Free Newton-Type Method for Solving Nonlinear Equations, Applied Mathematics & Information Sciences an International Journal,Vol.9(3), pp. 1507-1513.
XIV. Somroo, E., (2016), On the Development of a New Multi-Step Derivative Free Method to Accelerate the Convergence of Bracketing Methods for Solving, Sindh University Research Journal (Sci. Ser.) Vol. 48(3), pp. 601-604.
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XVI. Umer, S., M. M. Shaikh, A. W. 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.
XVII. Weerakoon, S. And T. G. I. Fernando, A Variant of Newton’ s Method with Accelerated Third-Order Convergence, Applied Mathematics Letters Vol. 13, pp. 87-93.

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