On an approximate solution of a boundary value problem for a nonlinear integro-differential equation

Joint Authors

Yusuf, Muhammad I.
Abduh, Muhammad A.

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

Mathematics

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 I.. 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 I.. 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 I.. 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