Geometric numerical integration

Ernst Hairer, Christian Lubich, Gerhard Wanner
Springer
 9783540306634
3-540-30663-3

This book covers numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions. It presents a.

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theory of symplectic and symmetric methods, which include various specially designed integrators, as well as discusses their construction and practical merits. The long-time behavior of the numerical solutions is studied using a backward error analysis combined with KAM theory.