Solving Linear Second-Order Singularly Perturbed Differential Difference Equations via Initial Value Method
Joint Authors
Melesse, Wondwosen Gebeyaw
Tiruneh, Awoke Andargie
Derese, Getachew Adamu
Source
International Journal of Differential Equations
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-11-22
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
In this paper, an initial value method for solving a class of linear second-order singularly perturbed differential difference equation containing mixed shifts is proposed.
In doing so, first, the given problem is modified in to an equivalent singularly perturbed problem by approximating the term containing the delay and advance parameters using Taylor series expansion.
From the modified problem, two explicit initial value problems which are independent of the perturbation parameter are produced; namely, the reduced problem and the boundary layer correction problem.
These problems are then solved analytically and/or numerically, and those solutions are combined to give an approximate solution to the original problem.
An error estimate for this method is derived using maximum norm.
Several test problems are considered to illustrate the theoretical results.
It is observed that the present method approximates the exact solution very well.
American Psychological Association (APA)
Melesse, Wondwosen Gebeyaw& Tiruneh, Awoke Andargie& Derese, Getachew Adamu. 2019. Solving Linear Second-Order Singularly Perturbed Differential Difference Equations via Initial Value Method. International Journal of Differential Equations،Vol. 2019, no. 2019, pp.1-10.
https://search.emarefa.net/detail/BIM-1159189
Modern Language Association (MLA)
Melesse, Wondwosen Gebeyaw…[et al.]. Solving Linear Second-Order Singularly Perturbed Differential Difference Equations via Initial Value Method. International Journal of Differential Equations No. 2019 (2019), pp.1-10.
https://search.emarefa.net/detail/BIM-1159189
American Medical Association (AMA)
Melesse, Wondwosen Gebeyaw& Tiruneh, Awoke Andargie& Derese, Getachew Adamu. Solving Linear Second-Order Singularly Perturbed Differential Difference Equations via Initial Value Method. International Journal of Differential Equations. 2019. Vol. 2019, no. 2019, pp.1-10.
https://search.emarefa.net/detail/BIM-1159189
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1159189