New Improved Variational Homotopy Perturbation Method for Bratu-Type Problems

Olusola Ezekiel Abolarin

doi:10.4236/ajcm.2013.32018

Olusola Ezekiel Abolarin

Open Access

https://doi.org/10.4236/ajcm.2013.32018

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Abstract

This research paper deals with the boundary and initial value problems for the Bratu-type model by using the New Improved Variational Homotopy Perturbation Method. The New Method does not require discritization, linearization or any restrictive assumption of any form in providing analytical or approximate solutions to linear and nonlinear equation without the integral related with nonlinear term. Theses virtues make it to be reliable and its efficiency is demonstrated with numerical examples.

Highlights

The Bratu-type boundary value problem in one-dimensional planar coordinates u eu 0 (1.1)u 0 u 1 0 arises from a simplification of the solid fuel ignition model in thermal combustion theory, physical applications ranging from chemical reaction theory, radiative heat transfer and nanotechnology to the expansion of universe [1,2,3,4,5]
The existing methods such as Adomian decomposition method, variational iteration method and homotopy perturbation method involve the computation of Adomian polynomials, and the integral related with eu or the perturbation of small parameters, this leads to increase the numerical computation cost and narrow down their applications
In order to improve on what Lin Jin [9] has done, we introduce the New Improved Variational Homotopy Perturbation Method for Bratu-Type Problems which is a time cost effective and uses friendly

Summary

Introduction

The Bratu-type boundary value problem in one-dimensional planar coordinates u eu 0. The existing methods such as Adomian decomposition method, variational iteration method and homotopy perturbation method involve the computation of Adomian polynomials, and the integral related with eu or the perturbation of small parameters, this leads to increase the numerical computation cost and narrow down their applications. To avoid these disadvantages, Lin Jin [9] proposed a modified variational iteration method to solve the Bratu problems, based upon the Taylor series expansion. In order to improve on what Lin Jin [9] has done, we introduce the New Improved Variational Homotopy Perturbation Method for Bratu-Type Problems which is a time cost effective and uses friendly

Variational Iteration Method and Its Modification

New Imprved Variational Homotopy Perturbation Method

Numerical Examples

Conclusion