Abstract
This chapter is devoted to practical aspects of an implementation of geometric integrators. We explain strategies for changing the step size which do not deteriorate the correct qualitative behaviour of the solution. We study multiple time stepping strategies, the effect of round-off in long-time integrations, and the efficient solution of nonlinear systems arising in implicit integration schemes.
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References
Laburta (1997) proposes to consider m= 2, µl = 0, µ2 = 1 (apart from the first step this also needs only one additional function evaluation per step), and to optimize free parameters by satisfying the order conditions for some trees with one order higher.
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© 2002 Springer-Verlag Berlin Heidelberg
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Hairer, E., Wanner, G., Lubich, C. (2002). Structure-Preserving Implementation. In: Geometric Numerical Integration. Springer Series in Computational Mathematics, vol 31. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05018-7_8
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DOI: https://doi.org/10.1007/978-3-662-05018-7_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-05020-0
Online ISBN: 978-3-662-05018-7
eBook Packages: Springer Book Archive