Modified DJ method: Application to Boussinesq equation

TL;DR

This paper introduces a modified DJ method that accelerates convergence for solving nonlinear equations and demonstrates its effectiveness by obtaining more accurate analytical solutions to the Boussinesq equation compared to existing methods.

Contribution

The paper presents a novel modification of the DJ method that improves convergence speed and accuracy in solving nonlinear equations, specifically applied to the Boussinesq equation.

Findings

The modified DJ method converges faster than the original.

It produces more accurate solutions than other iterative methods.

The method effectively solves the Boussinesq equation with lower error.

Abstract

In this paper we present a modification of DJ Method [J. Math. Anal. Appl. 316 (2006), 753-763] to solve the nonlinear equations more efficiently. It is observed that the modified DJ method is faster and hence it has accelerated convergence rate as compared to the old one. We use this new method to find the analytical solutions of Boussinesq equation. The reported results are compared with the exact solutions. Further, we compare the absolute error in our solution with those in other iterative methods. It is observed that the presented method is simple and generates more accurate solutions as compared with other methods.