Improved approximation algorithm for solution of nonlinear partial differential equations

TL;DR

This paper introduces a novel fixed grid size algorithm for the Reduced Differential Transform Method (RDTM) to efficiently approximate solutions of nonlinear partial differential equations, validated on heat and Burgers equations.

Contribution

It develops the first fixed grid size algorithm for RDTM, enhancing its efficiency and applicability to nonlinear PDEs.

Findings

The new RDTM algorithm produces solutions consistent with exact solutions.

Application to heat and Burgers equations demonstrates the method's effectiveness.

The method improves approximation accuracy over existing approaches.

Abstract

In this study,a new method was presented by developing Reduced differential transform method in order to find approximate solution of partial differential equations. Here, RDTM with fixed grid size algorithm was developed for the first time for Reduced Differential Transform Method by dividing solution intervals given to us into fixed grids. The efficiency and advantage of this method was given in homogenous heat equation existing in literature and in the application part on Burgers equation. When approximate solution obtained by this new method and known exact solutions were compared, it is seen that there is definite consistence between both two solutions.