On the error analysis of the numerical solution of linear Volterra integral equations of the second kind

Abstract

In the numerical solution of linear Volterra integral equations, two kinds of errors occur. If we use the collocation method, these errors are the collocation and numerical quadrature errors. Each error has its own effect in the accuracy of the obtained numerical solution. In this study we obtain an error bound that is sum of these two errors and using this error bound the relation between the smoothness of the kernel in the equation and also the length of the integration interval and each of these two errors are considered. Concluded results also are observed during the solution of some numerical examples.

Keywords:

• Volterra integral equations
• collocation method
• numerical integration
• Chebyshev polynomials

2000 AMS Subject Classifications:

• 45D05
• 65L60
• 65D30
• 11R09