03174cam a22003734a 450000100090000000300080000900500170001700600190003400800410005301000170009402000300011104000220014104100080016308200290017110000240020024501580022425000190038226400480040130000470044949000660049650000190056250400660058150507380064752010200138565000480240565000250245365000260247865000250250465000230252970000370255270000280258985600910261785600920270816095817EC-UrYT20200513144338.0s||||gr|||| 00| 00100218s2010 gw a b 001 0 eng a 2010922987 a9783642051579 (softcover) aDLCcDLCdEC-UrYT aeng 221a515.352bH1537g 20101 aHairer, E.q(Ernst)10aGeometric numerical integration :bstructure-preserving algorithms for ordinary differential equations /cErnst Hairer, Christian Lubich, Gerhard Wanner. aSecond edition34aHeidelberg ;aNew York :bSpringer,cc2010. axvii, 644 pages :billustrations ;c25 cm. aSpringer series in computational mathematicsx0179-3632 ;v31 aInclude index aIncludes bibliographical references (p. [617]-636) and index.2 aExamples and numerical experiments -- Numerical integrators -- Order conditions, trees and B-series -- Conservation of first integrals and methods on manifolds -- Symmetric integration and reversibility -- Symplectic integration of Hamiltonian systems -- Non-canonical Hamiltonian systems -- Structure-preserving implementation -- Backward error analysis and structure preservation -- Hamiltonian perturbation theory and symplectic integrators -- Reversible perturbation theory and symmetric integrators -- Dissipative perturbed Hamiltonian and reversible systems -- Oscillatory diffential equations with constant high frequencies -- Oscillatory differential equations with varying high frequencies -- Dynamics of multistep methods. 3 a
Numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions are the subject of this book. A complete self-contained theory of symplectic and symmetric methods, which include Runge-Kutta, composition, splitting, multistep and various specially designed integrators, is presented and their construction and practical merits are discussed. The long-time behaviour of the numerical solutions is studied using a backward error analysis (modified equations) combined with KAM theory. The book is illustrated by many figures, it treats applications from physics and astronomy and contains many numerical experiments and comparisons of different approaches. The second edition is substantially revised and enlarged, with many improvements in the presentation and additions concerning in particular non-canonical Hamiltonian systems, highly oscillatory mechanical systems, and the dynamics of multistep methods. 0aDifferential equationsxNumerical solutions 0aHamiltonian systems. 0aNumerical integration 0aMathematical physics 0aNumerical analysis1 aLubich, Christiand1959-eauthor1 aWanner, Gerhardeauthor423Publisher descriptionuhttp://www.loc.gov/catdir/enhancements/fy1317/2010922987-d.html413Table of contents onlyuhttp://www.loc.gov/catdir/enhancements/fy1402/2010922987-t.html