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Piecewise Approximate Analytical Solutions of High-Order Singular Perturbation Problems with a Discontinuous Source Term
Author
Source
International Journal of Differential Equations
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-11-15
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
El-Zahar, Essam R.. 2016. Piecewise Approximate Analytical Solutions of High-Order Singular Perturbation Problems with a Discontinuous Source Term. International Journal of Differential Equations،Vol. 2016, no. 2016, pp.1-12.
https://search.emarefa.net/detail/BIM-1105681
Modern Language Association (MLA)
El-Zahar, Essam R.. Piecewise Approximate Analytical Solutions of High-Order Singular Perturbation Problems with a Discontinuous Source Term. International Journal of Differential Equations No. 2016 (2016), pp.1-12.
https://search.emarefa.net/detail/BIM-1105681
American Medical Association (AMA)
El-Zahar, Essam R.. Piecewise Approximate Analytical Solutions of High-Order Singular Perturbation Problems with a Discontinuous Source Term. International Journal of Differential Equations. 2016. Vol. 2016, no. 2016, pp.1-12.
https://search.emarefa.net/detail/BIM-1105681
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1105681