A general framework for conservative single-step time-integration schemes with higher-order accuracy for a central-force system
✍ Scribed by E. Graham; G. Jelenić
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 519 KB
- Volume
- 192
- Category
- Article
- ISSN
- 0045-7825
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✦ Synopsis
A general framework for algorithms that conserve angular momentum for single-body central-force problems is presented. It is shown that any family of momentum-conserving algorithms can have at most three free parameters, one of which may be used to ensure energy conservation (and hence will be configuration-dependent). Further restrictions can be made that enable the algorithms to recover the orbits of relative equilibria of the underlying physical problem. In addition, the algorithms can be made time-reversible, whilst still leaving two parameters unspecified. The order of accuracy of a general momentum-conserving family is analysed, and it is shown that energy-momentum algorithms that preserve the underlying physical relative equilibria can have unlimited accuracy if the two remaining parameters are appropriately chosen functions of the configuration and the time-step: this does not require any additional degrees of freedom, extra stages of calculation or information from past solutions. Numerical examples are given that show the performance of some representative higher-order schemes when applied to stiff and non-stiff problems, and the issue of Newton-Raphson convergence is discussed.