Collocation Methods for Volterra Integral and Integro-Differential Equations: A Review

Abstract

We present a collection of recent results on the numerical approximation of Volterra integral equations and integro-differential equations by means of collocation type methods, which are able to provide better balances between accuracy and stability demanding. We consider both exact and discretized one-step and multistep collocation methods, and illustrate main convergence results, making some comparisons in terms of accuracy and efficiency. Some numerical experiments complete the paper.

Keywords

• Volterra integral equations
• Volterra integro–differential equations
• collocation methods
• multistep methods
• convergence