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

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.Comment: 14p, 5 fig