MARC Record from harvard_bibliographic_metadata

LEADER: 03149cam a2200421 a 4500
001 010113534-3
005 20140919093406.0
008 060410s2006 gw a b 001 0 eng c
010 $a 2005938386
020 $a3540306633
020 $a9783540306634
035 0 $aocm69223213
040 $aCSt$cSTF$dBAKER$dIXA
042 $apcc
050 4 $aQA299.3$b.H35 2006
100 1 $aHairer, E.$q(Ernst)
245 10 $aGeometric numerical integration :$bstructure-preserving algorithms for ordinary differential equations /$cErnst Hairer, Christian Lubich, Gerhard Wanner.
250 $a2nd ed.
260 $aBerlin ;$aNew York :$bSpringer,$cc2006.
300 $axvii, 644 p. :$bill. ;$c25 cm.
490 1 $aSpringer series in computational mathematics,$x0179-3632 ;$v31
504 $aIncludes bibliographical references (p. [617]-636) and index.
505 0 $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 -- Dissipatively Perturbed Hamiltonian and Reversible Systems -- Oscillatory Differential Equations with Constant High Frequencies -- Oscillatory Differential Equations with Varying High Frequencies -- Dynamics of Multistep Methods.
520 $aNumerical 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.
650 0 $aNumerical integration.
650 0 $aHamiltonian systems.
650 0 $aDifferential equations$xNumerical solutions.
650 0 $aBiology$xMathematics.
650 0 $aGlobal analysis (Mathematics).
650 0 $aMathematical physics.
650 0 $aMathematics.
650 0 $aNumerical analysis.
650 0 $aPhysics.
700 1 $aLubich, Christian,$d1959-
700 1 $aWanner, Gerhard.
830 0 $aSpringer series in computational mathematics ;$v31.
988 $a20060925
906 $0OCLC