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

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Structure-Preserving Implementation,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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dBASE IV Lernen am Konkreten Beispielsses 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

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https://doi.org/10.1007/978-3-322-92882-5ed Runge–Kutta methods, and composition methods by using the notion of rooted trees and B-series. These ideas lead to algebraic structures which have recently found interesting applications in quantum field theory. The chapter terminates with the Baker- Campbell-Hausdorff formula, which allows anoth

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Arbeitsbereich und Datenausgabe,n manifolds. Our investigation will follow two directions. We first investigate which of the methods introduced in Chap. II conserve invariants automatically. We shall see that most of them conserve linear invariants, a few of them quadratic invariants, and none of them conserves cubic or general no

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