Approximate solution of systems of Volterra integral equations with error analysis

Abstract

This paper describes a procedure for solving the system of linear Volterra integral equations by means of the Sinc collocation method. A convergence and an error analysis are given; it is shown that the Sinc solution produces an error of order O(exp(−c N ^1/2)), where c>0 is a constant. This approximation reduces the system of integral equations to an explicit system of algebraic equations. The analytical results are illustrated with numerical examples that exhibit the exponential convergence rate.

Keywords:

• system of Volterra integral equations
• sinc method
• exponential convergence

2000 AMS Subject Classifications:

• 65R20
• 45A05
• 45D05
• 34A30

Acknowledgements

The authors thank the referees for their many valuable comments in help revising this paper.