Titlebook: Geometric Numerical Integration; Structure-Preserving Ernst Hairer,Gerhard Wanner,Christian Lubich Book 20021st edition Springer-Verlag Ber

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Die übrigen Kleearten bzw. Futterleguminosenthem. In particular, we study projection methods and methods based on local coordinates of the manifold defined by the invariants. We discuss in some detail the case where the manifold is a Lie group.

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Curt F. Kollbrunner,Nikola Hajdinion, which is a formal series in powers of the step size, has to be truncated. The error, induced by such a truncation, can be made exponentially small, and the results remain valid on exponentially long time intervals.

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Examples and Numerical Experiments,ffects (on a different scale) occur with more sophisticated higher-order integration schemes. The experiments presented here should serve as a motivation for the theoretical and practical investigations of later chapters. The reader is encouraged to repeat the experiments or to invent similar ones.

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Order Conditions, Trees and B-Series,recently found interesting applications in quantum field theory. The chapter terminates with the Baker-CampbellHausdorff formula, which allows another access to the order properties of composition and splitting methods.

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Symmetric Integration and Reversibility,Runge-Kutta and composition methods, and we show how standard approaches for solving differential equations on manifolds can be symmetrized. A theoretical explanation of the excellent longtime behaviour of symmetric methods applied to reversible differential equations will be given in Chap. XI.