Perturbation Iteration Transform Method for the Solution of Newell-Whitehead-Segel Model Equations

TL;DR

This paper introduces the Perturbation Iteration Transform Method (PITM), a new computational approach combining Laplace Transform and Perturbation Iteration to efficiently solve Newell-Whitehead-Segel equations, validated against exact and other semi-analytical solutions.

Contribution

The paper presents a novel hybrid method (PITM) for solving NWSEs, demonstrating its efficiency and reliability compared to existing semi-analytical techniques.

Findings

Results closely match exact solutions

Method outperforms some existing semi-analytical methods

Efficient computational implementation in Mathematica 10

Abstract

In this study, a computational method referred to as Perturbation Iteration Transform Method (PITM), which is a combination of the conventional Laplace Transform Method (LTM) and the Perturbation Iteration Algorithm (PIA) is applied for the solution of Newell-Whitehead- Segel Equations (NWSEs). Three unique examples are considered and the results obtained are compared with their exact solutions graphically. Also, the results agree with those obtained via other semi-analytical methods viz: New Iterative Method and Adomian Decomposition Method. This present method proves to be very efficient and reliable. Mathematica 10 is used for all the computations in this study.