Titlebook: Geometric Numerical Integration; Structure-Preserving Ernst Hairer,Gerhard Wanner,Christian Lubich Book 2006Latest edition Springer-Verlag

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https://doi.org/10.1007/978-3-642-59076-4not 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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Geometric Numerical Integration978-3-540-30666-5Series ISSN 0179-3632 Series E-ISSN 2198-3712

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Examples and Numerical Experiments,ods. We deliberately consider only very simple numerical methods of orders 1 and 2 to emphasize the qualitative aspects of the experiments. The same effects (on a different scale) occur with more sophisticated higher-order integration schemes. The experiments presented here should serve as a motivat

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Numerical Integrators,sses of numerical methods. We start with Runge–Kutta and collocation methods, and we introduce discontinuous collocation methods, which cover essentially all high-order implicit Runge–Kutta methods of interest. We then treat partitioned Runge–Kutta methods and Nyström methods, which can be applied t