Numerical solution of the second order linear and nonlinear integro-differential equations using Haar wavelet method

Joint Authors

Shah, Kamal
Mahariq, Ibrahim
Ruh al-Amin
al-Sayyid, Fahmi
Uways, Muhammad

Source

Arab Journal of Basic and Applied Sciences

Issue

Vol. 28, Issue 1 (31 Dec. 2021), pp.12-20, 9 p.

Publisher

University of Bahrain College of Science

Publication Date

2021-12-31

Country of Publication

Bahrain

No. of Pages

9

Main Subjects

Mathematics

Abstract EN

In this paper, a numerical algorithm is developed for the solution of second order linear and nonlinear integro-differential equations.

The Haar collocation technique is applied to second order linear and nonlinear integro-differential equations.

In Haar technique, the second order derivative in both linear and nonlinear integro-differential equation is approximated using Haar functions and the process of integration is used to obtain the expression of first order derivative and expression for the unknown function.

Some linear and nonlinear examples are taken from literature for checking validation and convergence of proposed technique.

The maximum absolute and root mean square errors are compared with the exact solution at different collocation and gauss points.

The convergence rate using different numbers of collocation points is also calculated, which is approximately equal to 2.

American Psychological Association (APA)

Ruh al-Amin& Mahariq, Ibrahim& Shah, Kamal& Uways, Muhammad& al-Sayyid, Fahmi. 2021. Numerical solution of the second order linear and nonlinear integro-differential equations using Haar wavelet method. Arab Journal of Basic and Applied Sciences،Vol. 28, no. 1, pp.12-20.
https://search.emarefa.net/detail/BIM-1340607

Modern Language Association (MLA)

Uways, Muhammad…[et al.]. Numerical solution of the second order linear and nonlinear integro-differential equations using Haar wavelet method. Arab Journal of Basic and Applied Sciences Vol. 28, no. 1 (2021), pp.12-20.
https://search.emarefa.net/detail/BIM-1340607

American Medical Association (AMA)

Ruh al-Amin& Mahariq, Ibrahim& Shah, Kamal& Uways, Muhammad& al-Sayyid, Fahmi. Numerical solution of the second order linear and nonlinear integro-differential equations using Haar wavelet method. Arab Journal of Basic and Applied Sciences. 2021. Vol. 28, no. 1, pp.12-20.
https://search.emarefa.net/detail/BIM-1340607

Data Type

Journal Articles

Language

English

Notes

Includes bibliographical references : p. 19-20

Record ID

BIM-1340607