Hairer E. Geometric Numerical Integration...Algorithms for ODE 2006

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The subject of this book is numerical methods that preserve geometric properties of the flow of a differential equation: symplectic integrators for Hamiltonian systems, symmetric integrators for reversible systems, methods preserving first integrals and numerical methods on manifolds, including Lie group methods and integrators for constrained mechanical systems, and methods for problems with highly oscillatory solutions. Structure preservation – with its questions as to where, how, and what for – is the unifying theme