# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1703.06745