Implementation of DIMSIMs for stiff differential systems

Zdzislaw Jackiewicz

doi:10.1016/S0168-9274(01)00154-4

Implementation of DIMSIMs for stiff differential systems

Zdzislaw Jackiewicz

CLAS-NS: Mathematics and Statistical Sciences, School of (SMSS)

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

25 Scopus citations

Abstract

Some issues related to the implementation of diagonally implicit multistage integration methods for stiff differential systems are discussed. They include reliable estimation of the local discretization error, construction of continuous interpolants, solution of nonlinear systems of equations by simplified Newton iterations, choice of initial stepsize and order, and step and order changing strategy. Numerical results are presented which indicate that an experimental Matlab code based on type 2 methods of order one, two and three outperforms ode15s code from Matlab ODE suite on problems whose Jacobian has eigenvalues which are close to the imaginary axis.

Original language	English (US)
Pages (from-to)	251-267
Number of pages	17
Journal	Applied Numerical Mathematics
Volume	42
Issue number	1-3
DOIs	https://doi.org/10.1016/S0168-9274(01)00154-4
State	Published - Aug 1 2002

Keywords

DIMSIMs
Local error estimation for stiff systems
Nordsieck representation
Simplified Newton iterations

ASJC Scopus subject areas

Numerical Analysis
Computational Mathematics
Applied Mathematics

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