Open AccessComparison Between Numerical Methods for Generalized Zakharov system
Author(s) -
A. M. Kawala,
H. K. Abdelaziz
Publication year - 2021
Publication title -
international journal of mathematical models and methods in applied sciences
Language(s) - English
Resource type - Journals
ISSN - 1998-0140
DOI - 10.46300/9101.2021.15.28
Subject(s) - legendre polynomials , mathematics , algebraic equation , taylor series , transformation (genetics) , collocation method , legendre function , legendre transformation , mathematical analysis , collocation (remote sensing) , algebraic number , associated legendre polynomials , series (stratigraphy) , differential equation , nonlinear system , classical orthogonal polynomials , orthogonal polynomials , ordinary differential equation , computer science , gegenbauer polynomials , biochemistry , chemistry , physics , paleontology , quantum mechanics , machine learning , biology , gene
We present two numerical methods to get approximate solutions for generalized Zakharov system GZS. The first one is Legendre collocation method, which assumes an expansion in a series of Legendre polynomials , for the function and its derivatives occurring in the GZS, the expansion coefficients are then determined by reducing the problem to a system of algebraic equations. The second is differential transform method DTM , it is a transformation technique based on the Taylor series expansion. In this method, certain transformation rules are applied to transform the problem into a set of algebraic equations and the solution of these algebraic equations gives the desired solution of the problem.The obtained numerical solutions compared with corresponding analytical solutions.The results show that the proposed method has high accuracy for solving the GZS.