Geometric Numerical Integration

Structure-Preserving Algorithms for Ordinary Differential Equations

Ranked #51 in Numerical Analysis, Ranked #52 in Differential Equations

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 atheory 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. less

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