Piecewise approximate analytical solutions of high-order singular perturbation problems with a discontinuous source term
type: Item
instance of: scholarly article
title: Piecewise approximate analytical solutions of high-order singular perturbation problems with a discontinuous source term
zbMATH Open document ID: 1459.34065
DOI: 10.1155/2016/1015634
author: E. R. El-Zahar
published in: International Journal of Differential Equations
publication date: 2018-08-10T00:00:00Z
review text: Summary: A reliable algorithm is presented to develop piecewise approximate analytical solutions of third- and fourth-order convection diffusion singular perturbation problems with a discontinuous source term. The algorithm is based on an asymptotic expansion approximation and differential transform method (DTM). First, the original problem is transformed into a weakly coupled system of ODEs and a zero-order asymptotic expansion of the solution is constructed. Then, a piecewise smooth solution of the terminal value reduced system is obtained by using DTM and imposing the continuity and smoothness conditions. The error estimate of the method is presented. The results show that the method is a reliable and convenient asymptotic semianalytical numerical method for treating high-order singular perturbation problems with a discontinuous source term.
Mathematics Subject Classification ID: 34A45
Mathematics Subject Classification ID: 34E05
zbMATH DE Number: 6915915
Wikidata QID: Q59124231
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/1015634
OpenAlex ID: W2555957384
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description: scientific article; zbMATH DE number 6915915