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Studies in the application of recurrence relations to special perturbation methods

VI: Comparison with classical single-step and multi-step methods of numerical integration

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Abstract

The numerical integration of the differential equations describing dynamical systems has been shown in previous papers of this series to be most effectively accomplished by an explicit Taylor series method.

In this paper we show that one explicit Taylor series method, developed earlier in this series and which appears to possess a high degree of versatility, yields considerable gains in efficiency over classical single-step and multi-step methods. (In this context efficiency is a measure of the time taken to carry out a calculation of a specific accuracy).

For a given accuracy criterion governing the local truncation error (LTE) it is found that the Taylor series method is generallytwice as fast as the classical multi-step method and up totwenty times faster than the classical single-step method.

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Authors and Affiliations

  1. Department of Astronomy, The University, G12 8QQ, Glasgow, Scotland, UK

    Hugo E. Schwarz & Ian W. Walker

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  1. Hugo E. Schwarz
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  2. Ian W. Walker
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Schwarz, H.E., Walker, I.W. Studies in the application of recurrence relations to special perturbation methods. Celestial Mechanics 27, 191–202 (1982). https://doi.org/10.1007/BF01271693

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  • DOI: https://doi.org/10.1007/BF01271693

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