Springer Series in Computational Mathematics 31: Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations, Second Edition (Hardback)
VERY GOOD: The book is in very good condition, showing only slight signs of use and wear. The binding is tight and the pages are clean. It is printed on acid-free paper.
Product Details
From the back cover: "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."
BRIEF CONTENTS
I. Examples and Numerical Experiments
II. Numerical Integrators
III. Order Condition, Trees and B-Trees
IV. Conservation of First Integrals and Methods on Manifolds
V. Symmetric Integration and Reversibility
VI. Symplectic Integration of Hamiltonian Systems
VII. Non-Canonical Hamiltonian Systems
VIII. Structure-Preserving Implementation
IX. Backward Error Analysis and Structure Preservation
X. Hamiltonian Perturbation Theory and Symplectic Integrators
XI. Reversible Perturbation Theory and Symmetric Integrators
XII. Dissipatively Perturbed Hamiltonian and Reversible Systems
XIII. Oscillatory Differential Equations with Constant High Frequencies
XIV. Oscillatory Differential Equations with Varying High Frequency
