Optimal Perturbation Iteration Method for Bratu-Type Problems

TL;DR

This paper presents an optimal perturbation iteration method that efficiently solves nonlinear differential equations, demonstrated on Bratu-type problems, achieving high accuracy with few terms compared to existing methods.

Contribution

The paper introduces a novel optimal perturbation iteration method that improves accuracy and efficiency in solving nonlinear differential equations, specifically applied to Bratu-type problems.

Findings

Requires fewer terms for accurate solutions

Outperforms many existing methods in literature

Demonstrates high efficiency and accuracy

Abstract

In this paper, we introduce the new optimal perturbation iteration method based on the perturbation iteration algorithms for the approximate solutions of nonlinear differential equations of many types. The proposed method is illustrated by studying Bratu-type equations. Our results show that only a few terms are required to obtain an approximate solution which is more accurate and efficient than many other methods in the literature.