International Journal of Differential Equations

Piecewise Approximate Analytical Solutions of High-Order Singular Perturbation Problems with a Discontinuous Source Term

Essam R. El-Zahar

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Abstract

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.

Article information

Source
Int. J. Differ. Equ., Volume 2016 (2016), Article ID 1015634, 12 pages.

Dates
Received: 29 July 2016
Accepted: 5 October 2016
First available in Project Euclid: 21 December 2016

Permanent link to this document
https://projecteuclid.org/euclid.ijde/1482352602

Digital Object Identifier
doi:10.1155/2016/1015634

Mathematical Reviews number (MathSciNet)
MR3576086

Zentralblatt MATH identifier
06915915

Citation

El-Zahar, Essam R. Piecewise Approximate Analytical Solutions of High-Order Singular Perturbation Problems with a Discontinuous Source Term. Int. J. Differ. Equ. 2016 (2016), Article ID 1015634, 12 pages. doi:10.1155/2016/1015634. https://projecteuclid.org/euclid.ijde/1482352602


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