Approximate Solution of Generalized Modified b-Equation by Optimal Auxiliary Function Method

Aatif Ali,Rashid Nawaz,Laiq Zada

doi:10.54938/ijemdm.2022.01.1.2

Abstract

In this study, the implantation of a new semi-analytical method called the optimal auxiliary function method (OAFM) has been extended to partial differential equations. The adopted method was tested upon for approximate solution of generalized modified b-equation. The first-order numerical solution obtained by OAFM has been compared with the variational homotopy perturbation method (VHPM). The method possesses the auxiliary function and control parameters which can be easily handled during simulation of the nonlinear problem. From the numerical and graphical results, we concluded the method is very effective and easy to implement for the nonlinear PDEs.

Highlights

Differential equations (DE) play a vital role in applied science and engineering
In the same research field, we extend the implementation of the optimal auxiliary function method (OAFM) partial differential equations and applied for the approximate solution of modified b-equation
The extended for of OAFM for partial differential equation has been discussed in the following steps

Summary

Introduction

Differential equations (DE) play a vital role in applied science and engineering. PDEs have a variety of applications in optics, hydrodynamics electromagnetism, economics, financial mathematics, and computer science. Nonlinear PDEs don’t have the exact solutions, the researchers adopted different approaches for the approximate solution. In such difficult cases, it’s so much tough to obtain the exact solution of these nonlinear differential equations. In the same research field, we extend the implementation of the OAFM partial differential equations and applied for the approximate solution of modified b-equation. This planed method was introduced by Marinca et al and used for the solution for the fluid model [6]. The modified b-equation has been studied by different methods in the series of papers [12,13,14]

OAFM Methodology for PDEs

Applications of the Method

Numerical Results