Numerical analysis and computational solution of integro-differential equations

Hermann BRUNNER*

*Corresponding author for this work

Research output: Chapter in book/report/conference proceedingChapterpeer-review

2 Citations (Scopus)

Abstract

The aim of this paper is to describe the current state of the numerical analysis and the computational solution of non-standard integro-differential equations of Volterra and Fredholmtypes that arise in various applications. In order to do so, we first give a brief review of recent results concerning the numerical analysis of standard (ordinary and partial) Volterra and Fredholmintegro-differential equations, with the focus being on collocation and (continuous and discontinuous) Galerkin methods. In the second part of the paper we look at the extension of these results to various classes of non-standard integro-differential equations type that arise as mathematical models in applications. We shall see that in addition to numerous open problems in the numerical analysis of such equations, many challenges in the computational solution of non-standard Volterra and Fredholm integro-differential equations are waiting to be addressed.

Original languageEnglish
Title of host publicationContemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan
PublisherSpringer International Publishing
Pages205-231
Number of pages27
ISBN (Electronic)9783319724560
ISBN (Print)9783319724553
DOIs
Publication statusPublished - 23 May 2018

Scopus Subject Areas

  • Mathematics(all)

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