Research Article | OPEN ACCESS
Cubic B-spline for the Numerical Solution of Parabolic Integro-differential Equation with a Weakly Singular Kernel
Shahid S. Siddiqi and Saima Arshed
Department of Mathematics, University of the Punjab, Lahore 54590, Pakistan
Research Journal of Applied Sciences, Engineering and Technology 2014 10:2065-2073
Received: June 28, 2013 | Accepted: July 19, 2013 | Published: March 15, 2014
Abstract
The aim of study is to solve parabolic integro-differential equation with a weakly singular kernel. Problems involving partial integro-differential equations arise in fluid dynamics, viscoelasticity, engineering, mathematical biology, financial mathematics and other areas. Many mathematical formulations of physical phenomena contain integro-differential equations. Integro-differential equations are usually difficult to solve analytically so, it is required to obtain an efficient approximate solution. A numerical method is developed to solve the partial integro-differential equation using the cubic B-spline collocation method. The method is based on discretizing the time derivative using finite central difference formula and the cubic B-spline collocation method for the spatial derivative. Three examples are considered to illustrate the efficiency of the method developed. It is to be observed that the numerical results obtained by the proposed method efficiently approximate the exact solutions.
Keywords:
Central differences, collocation method, cubic B-spline, integro-differential equation, weakly singular kernel,
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Competing interests
The authors have no competing interests.
Open Access Policy
This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Copyright
The authors have no competing interests.
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