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One step integration methods of third-fourth order accuracy with large hyperbolic stability limits

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  • Kinnmark, Ingemar P.E.
  • Gray, William G.

Abstract

One step integration methods of third and fourth order accuracy that use K function evaluations to solve the system of differential equations dydt= A · y are proposed. These methods are shown to have a hyperbolic stability limit of y (K − 1)2 − 1 which approaches the theoretical maximum limit of K − 1 at large K obtained for methods of lower order accuracy.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:26:y:1984:i:3:p:181-188
    DOI: 10.1016/0378-4754(84)90056-9
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    Cited by:

    1. 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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    1. 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.
    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.

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