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New stability theorems concerning one-step numerical methods for ordinary differential equations

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  • Vichnevetsky, R.

Abstract

A measure of the stability properties of numerical integration methods for ordinary differential equations is provided by their stability region, which is that region in the complex (Δtλ) plane for which a given method is stable when applied to the differential equation dydt=λy with a time-step Δt.

Suggested Citation

  • Vichnevetsky, R., 1983. "New stability theorems concerning one-step numerical methods for ordinary differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 25(3), pages 199-205.
    • Handle: RePEc:eee:matcom:v:25:y:1983:i:3:p:199-205
    DOI: 10.1016/0378-4754(83)90092-7
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    References listed on IDEAS

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    1. Vichnevetsky, R., 1979. "Stability charts in the numerical approximation of partial differential equations: a review," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 21(2), pages 170-177.
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    Cited by:

    1. Kinnmark, Ingemar P.E. & Gray, William G., 1984. "One step integration methods of third-fourth order accuracy with large hyperbolic stability limits," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 26(3), pages 181-188.
    2. Kinnmark, Ingemar P.E. & Gray, William G., 1984. "One step integration methods with maximum stability regions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 26(2), pages 87-92.
    3. Kinnmark, Ingemar P.E., 1987. "A principle for construction of one-step integration methods with maximum imaginary stability limits," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 29(2), pages 87-106.

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