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A Finite Difference Method and Effective Modification of Gradient Descent Optimization Algorithm for MHD Fluid Flow Over a Linearly Stretching Surface

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Computers, Materials & Continua 2020年第2期62卷 657-677页

作者： Yasir Nawaz Muhammad Shoaib Arif Mairaj Bibi Javeria Nawaz Abbasi Umer Javed Amna Nazeer Stochastic Analysis&Optimization Research Group Department of MathematicsAir UniversityPAF Complex E-9Islamabad44000Pakistan Department of Mathematics Comsats UniversityChak Shahzad CampusIslamabad44000Pakistan Department of Electrical and Computer Engineering Comsats UniversityIslamabadWah CampusWah Cantt47040Pakistan

Present contribution is concerned with the construction and application of a numerical method for the fluid flow problem over a linearly stretching surface with the modification of standard Gradient descent Algorithm to solve the resulted difference *** flow problem is constructed using continuity,and Navier Stoke equations and these PDEs are further converted into boundary value problem by applying suitable similarity transformations.A central finite difference method is proposed that gives third-order accuracy using three grid *** stability conditions of the present proposed method using a Gauss-Seidel iterative procedure is found using Von-Neumann stability criteria and order of the finite difference method is proved by applying the Taylor series on the discretised *** comparison of the presently modified optimisation algorithm with the Gauss-Seidel iterative method and standard Newton’s method in optimisation is also *** can be concluded that the presently modified optimisation Algorithm takes a few iterations to converge with a small value of the parameter contained in it compared with the standard descent algorithm that may take millions of iterations to *** present modification of the steepest descent method converges faster than Gauss-Seidel method and standard steepest descent method,and it may also overcome the deficiency of singular hessian arise in Newton’s method for some of the cases that may arise in optimisation problem(s).

关键词： Magnetohydrodynamic exact finite difference scheme optimization algorithm stability&convergence

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