Implementation of diagonally implicit multistage integration methods for ordinary differential equations

J. C. Butcher; Zdzislaw Jackiewicz

doi:10.1137/S0036142995282509

Implementation of diagonally implicit multistage integration methods for ordinary differential equations

J. C. Butcher, Zdzislaw Jackiewicz

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

63 Scopus citations

Abstract

We investigate the implementation of diagonally implicit multistage integration methods (DIMSIMs). The implementation issues addressed are the local error estimation, changing stepsize using the Nordsieck technique, and the construction of continuous interpolants. Numerical experiments with a method of order three indicate that the error estimates that have been constructed are very reliable in both a fixed and a variable stepsize environment.

Original language	English (US)
Pages (from-to)	2119-2141
Number of pages	23
Journal	SIAM Journal on Numerical Analysis
Volume	34
Issue number	6
DOIs	https://doi.org/10.1137/S0036142995282509
State	Published - Jan 1 1997

Keywords

Continuous interpolants
General linear method
Local error estimation
Nordsieck technique

ASJC Scopus subject areas

Numerical Analysis
Computational Mathematics
Applied Mathematics

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10.1137/S0036142995282509

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abstract = "We investigate the implementation of diagonally implicit multistage integration methods (DIMSIMs). The implementation issues addressed are the local error estimation, changing stepsize using the Nordsieck technique, and the construction of continuous interpolants. Numerical experiments with a method of order three indicate that the error estimates that have been constructed are very reliable in both a fixed and a variable stepsize environment.",

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AB - We investigate the implementation of diagonally implicit multistage integration methods (DIMSIMs). The implementation issues addressed are the local error estimation, changing stepsize using the Nordsieck technique, and the construction of continuous interpolants. Numerical experiments with a method of order three indicate that the error estimates that have been constructed are very reliable in both a fixed and a variable stepsize environment.

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KW - Local error estimation

KW - Nordsieck technique

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Implementation of diagonally implicit multistage integration methods for ordinary differential equations

Abstract

Keywords

ASJC Scopus subject areas

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