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Recent developments in stability and error analysis of numerical methods for ordinary differential equations

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Equadiff 82

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1017))

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Abstract

We survey recent theoretical work on four types of integration methods for ordinary differential equations: multistep-, one-leg-, Runge-Kutta-, and extrapolation methods. Rigorous stability results and error bounds were obtained for such methods as applied to the linear test equation with constant or variable coefficient and/or certain classes of nonlinear systems, notably dissipative (monotone negative) ones. Investigations were carried out both for constant and variable steps.

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Authors and Affiliations

  1. IBM Thomas J. Watson Research Center, 10598, Yorktown Heights, New York

    Werner Liniger

Authors
  1. Werner Liniger
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H. W. Knobloch Klaus Schmitt

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© 1983 Springer-Verlag

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Liniger, W. (1983). Recent developments in stability and error analysis of numerical methods for ordinary differential equations. In: Knobloch, H.W., Schmitt, K. (eds) Equadiff 82. Lecture Notes in Mathematics, vol 1017. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0103268

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  • DOI: https://doi.org/10.1007/BFb0103268

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12686-7

  • Online ISBN: 978-3-540-38678-0

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