Adaptive Time-Stepping and Computational Stability

Research output: Contribution to journalArticle

Abstract

We investigate the effects of adaptive time-stepping and other algorithmic strategies on the computational stability of ODE codes. We show that carefully designed adaptive algorithms have a most significant impact on computational stability and reliability. A series of computational experiments with the standard implementation of Dassl and a modified version, including stepsize control based on digital filters, is used to demonstrate that relatively small algorithmic changes are able to extract a vastly better computational stability at no extra expense. The inherent performance and stability of Dassl are therefore much greater than the standard implementation seems to suggest.

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Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematics

Keywords

  • Computational stability stepsize control adaptive time-stepping PI control digital filters Dassl mathematical software algorithm analysis
Original languageEnglish
Pages (from-to)225-243
JournalJournal of Computational and Applied Mathematics
Volume185
Publication statusPublished - 2006
Publication categoryResearch
Peer-reviewedYes

Bibliographic note

The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Numerical Analysis (011015004)