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Evaluation of implicit formulas for the solution of ODEs

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Abstract

Implicit formulas are quite popular for the solution of ODEs. They seem to be necessary for the solution of stiff problems. An acceptance test must be made of the approximate solution of the algebraic equations arising in the evaluation of an implicit formula. A reliable way to make this test is presented. It offers many practical advantages over current tests.

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Authors and Affiliations

  1. Numerical Mathematics Division 5642, Sandia Laboratories, 87185, Albuquerque, New Mexico, U.S.A.

    L. F. Shampine

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  1. L. F. Shampine
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This article was sponsored by the U.S. Department of Energy under Contract DE-AC04-76PD00789. The submitted manuscript has been authored by a contractor of the United States Government under contract. Accordingly the U.S. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or to allow others to do so, for U.S. Government purposes.

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Shampine, L.F. Evaluation of implicit formulas for the solution of ODEs. BIT 19, 495–502 (1979). https://doi.org/10.1007/BF01931266

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  • DOI: https://doi.org/10.1007/BF01931266

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