On the bivariate spectral homotopy analysis method approach for solving nonlinear evolution partial differential equations
type: Item
instance of: scholarly article
title: On the bivariate spectral homotopy analysis method approach for solving nonlinear evolution partial differential equations
zbMATH Open document ID: 1469.35187
DOI: 10.1155/2014/350529
author: Xianqiang Yang
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: This paper presents a new application of the homotopy analysis method (HAM) for solving evolution equations described in terms of nonlinear partial differential equations (PDEs). The new approach, termed bivariate spectral homotopy analysis method (BISHAM), is based on the use of bivariate Lagrange interpolation in the so-called rule of solution expression of the HAM algorithm. The applicability of the new approach has been demonstrated by application on several examples of nonlinear evolution PDEs, namely, Fisher's, Burgers-Fisher's, Burger-Huxley's, and Fitzhugh-Nagumo's equations. Comparison with known exact results from literature has been used to confirm accuracy and effectiveness of the proposed method.
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35C05
zbMATH DE Number: 7022204
Wikidata QID: Q59036418
describes a project that uses: Matlab
describes a project that uses: BVPh
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/350529
OpenAlex ID: W2119572163
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description: scientific article; zbMATH DE number 7022204