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A Runge-Kutta starter for a multistep method for differential-algebraic systems with discontinuous effects. (English) Zbl 0837.65075

The authors consider the numerical solution of differential equations, for which multistep methods require frequent restarts (e.g., in the presence of discontinuities). Instead of starting each time with a first- order method and very small stepsizes, they suggest to start with higher- order approximations and larger stepsizes, taking the necessary information from a suitable Runge-Kutta method. For this purpose, they construct a 6-stage Runge-Kutta method of order 4, which provides third- order approximations at equidistant points. Numerical experiments with problems from multibody system dynamics illustrate the efficiency of the new procedure.
Reviewer: E.Hairer (Genève)

MSC:

65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
65L50 Mesh generation, refinement, and adaptive methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
70F10 \(n\)-body problems

Software:

MBSSIM; LSODE
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Full Text: DOI

References:

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