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Compact Finite Difference Schemes for Solving a Class of Weakly- Singular Partial Integro-differential Equations
Mathematical Sciences Letters • 2012
Publication Information
Authors
A. F. Soliman; A M.A. EL-ASYED; M. S. El-Azab
Keywords
weakly-singular partial integro-differential equations; Taylor's approximation; fourth order compact
finite difference scheme; collocation method.
Journal
Mathematical Sciences Letters
Publisher
Not Available
Volume
1
Issue
Not Available
Pages
53-60
publication.type
International
Paper Link
Not Available
Supplementary Materials
Not Available
Abstract
In this paper, we present a new approach to resolve linear weakly-singular partial integro-differential
equations by first removing the singularity using Taylor's approximation and transform the given partial integrodifferential
equations into an partial differential equation. After that the fourth order compact finite difference
scheme and collocation method is presented to obtain system of algebraic equations which solved to compute the
unknown function. The efficiency and accuracy of the method is validated by its application to several distinct test
problems which have exact solutions.
equations by first removing the singularity using Taylor's approximation and transform the given partial integrodifferential
equations into an partial differential equation. After that the fourth order compact finite difference
scheme and collocation method is presented to obtain system of algebraic equations which solved to compute the
unknown function. The efficiency and accuracy of the method is validated by its application to several distinct test
problems which have exact solutions.