Analysis of the Enright-Kamel partitioning method for stiff ODEs

D.J. Higham

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

The use of implicit formulae in the solution of stiff ODEs gives rise to systems of nonlinear equations which are usually solved iteratively by a modified Newton scheme. The linear algebra costs associated with such schemes may form a substantial part of the overall cost of the solution. The work of W. H. Enright and M. S. Kamel attempts to reduce the cost of the iteration by automatically transforming and partitioning the system. We provide new theoretical justification for this method in the case where the stiff eigenvalues of the Jacobian matrix used in the modified Newton iteration are small in number and well separated from the other eigenvalues. The theory of Y. Saad is introduced and adapted to show that the method uses the projection of the Jacobian onto a Krylov subspace which virtually contains the dominant subspace. This is shown to have favourable consequences. Numerical evidence is provided to support the theory.
LanguageEnglish
Pages1-14
Number of pages13
JournalIMA Journal of Numerical Analysis
Volume9
Issue number1
DOIs
Publication statusPublished - Jan 1989

Fingerprint

Stiff ODEs
Partitioning
Costs
Eigenvalue
Krylov Subspace
Linear algebra
Jacobian matrices
Newton Iteration
System of Nonlinear Equations
Jacobian matrix
Nonlinear equations
Justification
Subspace
Projection
Iteration

Keywords

  • nonlinear equations
  • numerical mathematics
  • Newton scheme
  • Krylov subspace

Cite this

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Analysis of the Enright-Kamel partitioning method for stiff ODEs. / Higham, D.J.

In: IMA Journal of Numerical Analysis, Vol. 9, No. 1, 01.1989, p. 1-14.

Research output: Contribution to journalArticle

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