Error propagation in an explicit and an implicit numerical method for Volterra integro-differential equations

TL;DR

This paper analyzes how errors propagate in explicit and implicit numerical methods for Volterra integro-differential equations, establishing error bounds and confirming first-order global accuracy through numerical examples.

Contribution

It provides a detailed comparison of error propagation and bounds for both explicit and implicit methods applied to Volterra equations, highlighting their first-order global accuracy.

Findings

Global error bounds are derived for both methods.

Both methods exhibit first-order global accuracy.

Numerical examples confirm theoretical results.

Abstract

We study error propagation in both an explicit and an implicit method for solving Volterra integro-differential equations. We determine the relationship between local and global errors. We derive upper bounds for the global error, and show that the global order for both methods is expected to be first-order. A few numerical examples illustrate our results.