A meshless Collocation Method for the Approximate Solution of a Partial Integro-differential Equation.

A. ALI; E. RAHMAN; Z. JAN; I. HUSSAIN; S. AHMAD

Author(s)

A. ALI Department of Mathematics, Islamia College Peshawar, Khyber Pakhtunkhwa, Pakistan

E. RAHMAN Department of Mathematics, Islamia College Peshawar, Khyber Pakhtunkhwa, Pakistan

Z. JAN Department of Computer Science, Islamia College Peshawar, Khyber Pakhtunkhwa, Pakistan

I. HUSSAIN Department of Basic Sciences & Islamiat, University of Engineering & Technology, Peshawar, Khyber Pakhtunkhwa, Pakistan

S. AHMAD Department of Mathematics, Islamia College Peshawar, Khyber Pakhtunkhwa, Pakistan

Abstract

In this paper, a radial basis functions based collocation technique is developed to approximate solution of a partial integrodifferential equation having a weakly singular kernel. The time derivative is approximated using backward finite difference approach while radial basis functions are collocated of over the spatial domain. Two types of radial basis functions namely Multiquadric and quantic are employed. Accuracy of the proposed method is evaluated in terms of and , and by taking various time step sizes and different number of collocation points in the spatial domain. Numerical results of four test problems from literature are provided to study the accuracy and applicability of this method. Sufficient simulations are done to validate the method. Comparison of the results is also made with an existing method from literature.

Publication Details

Page(s) 589-594

DOI DOI not available

Published Journal: Sindh University Research Journal, Volume: 48, Issue: 3, Year: 2016

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