Open AccessRecent Modification of Decomposition Method for Solving Nonlinear Partial Differential Equations
Author(s) -
Z. H. Kareem,
L. N. M. Tawfiq
Publication year - 2020
Publication title -
journal of advances in mathematics
Language(s) - English
Resource type - Journals
ISSN - 2347-1921
DOI - 10.24297/jam.v18i.8744
Subject(s) - mathematics , discretization , linearization , nonlinear system , partial differential equation , simple (philosophy) , series (stratigraphy) , convergent series , computation , decomposition , decomposition method (queueing theory) , mathematical optimization , mathematical analysis , algorithm , power series , discrete mathematics , paleontology , philosophy , ecology , physics , epistemology , quantum mechanics , biology
In this paper, efficient modification of Adomain decomposition method is proposed to solve nonlinear partial differential equations. Yields solution in rapid convergent series from easily computable terms to get exact solution, and yields in few iterations we get exact solution. Moreover, this modification does not require any linearization, discretization, or perturbations and therefore reduces the computations. Two illustration examples are introduced and illustrate the procedure of modification is simple yet highly accurate and rapidly converge to exact solution compares with the ADM or other modifications. The methodology presented here is useful for strongly nonlinear problems.