A complete relief of the zero-stability domain

Abstract

This paper completes a series of three papers concerned with automatic selection of multistep methods with stability regions fitted with the eigenvalues of a Jacobian matrix of an ordinary differential system. Here the treatment is extended to cover the case of purely imaginary eigenvalues. The class of multistep methods has k steps, order k+l and depends on k−1 free parameters, which vary within the zero-stability domain [IML0001].A "relief" of [IML0002] is then provided in the sense that fromthe position of the parameters in [IML0003] we obtain an a priori picture of the stability region. Based on the relief of [IML0004], we derive an automatic selection criterion. Computational experience has indicated the efficiency of the procedure.

Keywords:

• Multistep method
• zero-stability
• optimal methods

AMS:

• 65L05

^∗This work has been supported by Junta Nacional de Investigaçäo Cientifica e Tecnológica and Instituto Nacional de Investigaçäo Cientifica.

^∗This work has been supported by Junta Nacional de Investigaçäo Cientifica e Tecnológica and Instituto Nacional de Investigaçäo Cientifica.

Notes

^∗This work has been supported by Junta Nacional de Investigaçäo Cientifica e Tecnológica and Instituto Nacional de Investigaçäo Cientifica.

Additional information

Notes on contributors

Paula De Oliveira

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