An investigation of optimally stable numerical integration methods with application to real time simulation

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Abstract
An approach for deriving numerical integration methods which possess extended ranges of absolute stability and arbitrarily small truncation error coefficients is given. In particular, a family of three-step methods which have these properties and which are classical to the second degree is derived. The derivation of this family of meth ods forms a generalization of a corresponding family of methods which have extended ranges of absolute sta bility and are classical to the third degree. Suitable perturbations of the coefficients of these methods allow their reduced range of relative stability to be increased and the resulting techniques may be considered to be optimum from the stability viewpoint. Such methods have particular application in real-time simulation where we seek maximum integration steps. The complete derivation scheme employed has gen eral application in the construction of numerical integra tion algorithms of arbitrary step number.

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