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

2023/07/23 by J.S.C. Prentice, Prentice, J. S. C.
Mathematics · #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2307.12196

openalex publication_date 2023/07/23 · openalex created_date 2023/07/26 · openalex updated_date 2026/07/28

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.

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