Numerical solution of fourth-order integro-differential equations using Chebyshev cardinal functions

Abstract

A numerical technique is presented for the solution of fourth-order integro-differential equations. This method uses the Chebyshev cardinal functions. The method consists of expanding the required approximate solution as the elements of Chebyshev cardinal functions. Using the operational matrix of derivative, we reduce the problem to a set of algebraic equations. Some numerical examples are included to demonstrate the validity and applicability of the technique. The method is easy to implement and produces very accurate results.

Keywords:

• integro-differential equations
• chebyshev cardinal functions
• operational matrix of derivative

2000 AMS Subject Classifications: :

• 65R20
• 65M60
• 65M70
• 45K05
• 45J05

Acknowledgements

The authors are very grateful to one of the referees for carefully reading the paper and for his(her) constructive comments and suggestions.