Implementation of DIMSIMs for stiff differential systems

Research output: Contribution to journalArticle

22 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 languageEnglish (US)
Pages (from-to)251-267
Number of pages17
JournalApplied Numerical Mathematics
Volume42
Issue number1-3
DOIs
StatePublished - 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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