Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-05T15:05:54.016Z Has data issue: false hasContentIssue false

A COMPUTATIONAL METHOD FOR SOLVING TWO-DIMENSIONAL LINEAR FREDHOLM INTEGRAL EQUATIONS OF THE SECOND KIND

Published online by Cambridge University Press:  01 April 2008

A. TARI*
Affiliation:
Faculty of Mathematical Science, University of Tabriz, Tabriz, Iran (email: [email protected]) Department of Mathematics, University of Shahed, Tehran, Iran (email: [email protected])
S. SHAHMORAD
Affiliation:
Faculty of Mathematical Science, University of Tabriz, Tabriz, Iran (email: [email protected])
*
For correspondence; e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper an expansion method, based on Legendre or any orthogonal polynomials, is developed to find numerical solutions of two-dimensional linear Fredholm integral equations. We estimate the error of the method, and present some numerical examples to demonstrate the accuracy of the method.

MSC classification

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2008

References

[1]Aliabdi, M. H. and Shahmorad, S., “A matrix formulation of the Tau method for Fredholm and Volterra linear integro-differential equations”, The Korean J. Comput. Appl. Math. 9(2) (2002) 497507.CrossRefGoogle Scholar
[2]Atkinson, K. E., The numerical solution of integral equations of the second kind (Cambridge University Press, Cambridge, 1997).CrossRefGoogle Scholar
[3]Delves, L. M. and Mohamed, J. L., Computational methods for integral equations (Cambridge University Press, Cambridge, 1985).CrossRefGoogle Scholar
[4]Hosseini, S. M. and Shahmorad, S., “Tau numerical solution of Fredholm integro-differential equations with arbitrary polynomial bases”, Appl. Math. Modeling 27 (2003) 145154.CrossRefGoogle Scholar
[5]Jain, M. K., Iyengar, S. R. K. and Jain, R. K., Numerical methods for scientific and engineering computation (Wiley Eastern Limited, New Delhi, 1987).Google Scholar
[6]Jerri, A. J., Introduction to integral equations with applications (John Wiley & Sons, New York, 1999).Google Scholar
[7]Kanwal, R. P., Linear integral equations (Academic Press, London, 1971).Google Scholar
[8]Kincaid, D. and Cheney, W., Numerical analysis: mathematics of scientific computing (Brooks Cole Publishing Company, CA, 1990).Google Scholar
[9]Kress, R., Linear integral equations (Springer, Berlin, 1999).CrossRefGoogle Scholar