Geometric integrators are time-stepping methods, designed such that
they exactly satisfy conservation laws, symmetries or symplectic
properties of a system of differential equations. In this book the
authors outline the principles of geometric integration and
demonstrate how they can be applied to provide efficient numerical
methods for simulating conservative models. Beginning from basic
principles and continuing with discussions regarding the
advantageous properties of such schemes, the book introduces
methods for the N-body problem, systems with holonomic constraints,
and rigid bodies. More advanced topics treated include high-order
and variable stepsize methods, schemes for treating problems
involving multiple time-scales, and applications to molecular
dynamics and partial differential equations. The emphasis is on
providing a unified theoretical framework as well as a practical
guide for users. The inclusion of examples, background material and
exercises enhance the usefulness of the book for self-instruction
or as a text for a graduate course on the subject.
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