Approximations of Time-Dependent Nonlinear Partial Differential Equations using Galerkin Optimal Auxiliary Function Method

Autor:	Trisha, Nilormy Gupta, Islam, Md. Shafiqul
Rok vydání:	2023
Předmět:	Mathematics - Numerical Analysis 35K15 35K55 65M60 41A81
Druh dokumentu:	Working Paper
Popis:	The purpose of this research work is to employ the Optimal Auxiliary Function Method (OAFM) for obtaining numerical approximations of time-dependent nonlinear partial differential equations (PDEs) that arise in many disciplines of science and engineering. The initial and first approximations of parabolic nonlinear PDEs associated with initial conditions have been generated by utilizing this method. Then the Galerkin method is applied to estimate the coefficients that remain unknown. Finally, the values of the coefficients generated by the Galerkin method have been inserted into the first approximation. In each example, all numerical computations and corresponding absolute errors are provided in schematic and tabular representations. The rate of convergence attained by the proposed method is depicted in tabular form Comment: Accepted for Publication into the journal GANIT: Journal of Bangladesh Mathematical Society, 2023
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2306.06430 Zobrazit plný text záznamu View this record from Arxiv