@Article{cmc.2020.08584,
AUTHOR = {Yasir Nawaz, Muhammad Shoaib Arif , Mairaj Bibi, Javeria Nawaz Abbasi, Umer Javed, Amna Nazeer},
TITLE = {A Finite Difference Method and Effective Modification of Gradient Descent Optimization Algorithm for MHD Fluid Flow Over a Linearly Stretching Surface},
JOURNAL = {Computers, Materials \& Continua},
VOLUME = {62},
YEAR = {2020},
NUMBER = {2},
PAGES = {657--677},
URL = {http://www.techscience.com/cmc/v62n2/38269},
ISSN = {1546-2226},
ABSTRACT = {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).},
DOI = {10.32604/cmc.2020.08584}
}