TY - EJOU
AU - Nawaz, Yasir
AU - Arif, Muhammad Shoaib
AU - Bibi, Mairaj
AU - Abbasi, Javeria Nawaz
AU - Javed, Umer
AU - Nazeer, Amna
TI - A Finite Difference Method and Effective Modification of Gradient Descent Optimization Algorithm for MHD Fluid Flow Over a Linearly Stretching Surface
T2 - Computers, Materials \& Continua
PY - 2020
VL - 62
IS - 2
SN - 1546-2226
AB - 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
equation. The 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 points. The stability conditions of the present
proposed method using a Gauss-Seidel iterative procedure is found using VonNeumann stability criteria and order of the finite difference method is proved by
applying the Taylor series on the discretised equation. The comparison of the presently
modified optimisation algorithm with the Gauss-Seidel iterative method and standard
Newton’s method in optimisation is also made. It 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 converge. The 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).
KW - Magnetohydrodynamic
KW - exact finite difference scheme
KW - optimization algorithm
KW - stability & convergence
DO - 10.32604/cmc.2020.08584