On an approximate solution of a boundary value problem for a nonlinear integro-differential equation
Joint Authors
Abduh, Muhammad A.
Yusuf, Muhammad Ibrahim Muhammad
Source
Arab Journal of Basic and Applied Sciences
Issue
Vol. 28, Issue 1 (31 Dec. 2021), pp.386-396, 11 p.
Publisher
University of Bahrain College of Science
Publication Date
2021-12-31
Country of Publication
Bahrain
No. of Pages
11
Main Subjects
Abstract EN
The aim of this work is to discuss the solvability of a boundary value problem for a nonlinear integro-differential equation.
First, we derive an equivalent nonlinear Fredholm integral equation (NFIE) to this problem.
Second, we prove the existence of a solution to the NFIE using the Krasnosel’skii fixed point theorem under verifying some sufficient conditions.
Third, we solve the NFIE numerically and study the convergence rate via methods based upon applying the modified Adomian decomposition method and Liao’s homotopy analysis method.
As applications, some examples are illustrated to support our work.
The results in this work refer to both methods are efficient and converge rapidly, but the homotopy analysis method may converge faster when we succeed in choosing the optimal homotopy control parameter.
American Psychological Association (APA)
Abduh, Muhammad A.& Yusuf, Muhammad Ibrahim Muhammad. 2021. On an approximate solution of a boundary value problem for a nonlinear integro-differential equation. Arab Journal of Basic and Applied Sciences،Vol. 28, no. 1, pp.386-396.
https://search.emarefa.net/detail/BIM-1340643
Modern Language Association (MLA)
Abduh, Muhammad A.& Yusuf, Muhammad Ibrahim Muhammad. On an approximate solution of a boundary value problem for a nonlinear integro-differential equation. Arab Journal of Basic and Applied Sciences Vol. 28, no. 1 (2021), pp.386-396.
https://search.emarefa.net/detail/BIM-1340643
American Medical Association (AMA)
Abduh, Muhammad A.& Yusuf, Muhammad Ibrahim Muhammad. On an approximate solution of a boundary value problem for a nonlinear integro-differential equation. Arab Journal of Basic and Applied Sciences. 2021. Vol. 28, no. 1, pp.386-396.
https://search.emarefa.net/detail/BIM-1340643
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 396
Record ID
BIM-1340643