Ebook: Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations

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Content:
Front Matter....Pages i-xiii
Examples and Numerical Experiments....Pages 1-22
Numerical Integrators....Pages 23-46
Order Conditions, Trees and B-Series....Pages 47-92
Conservation of First Integrals and Methods on Manifolds....Pages 93-130
Symmetric Integration and Reversibility....Pages 131-166
Symplectic Integration of Hamiltonian Systems....Pages 167-208
Further Topics in Structure Preservation....Pages 209-254
Structure-Preserving Implementation....Pages 255-286
Backward Error Analysis and Structure Preservation....Pages 287-326
Hamiltonian Perturbation Theory and Symplectic Integrators....Pages 327-374
Reversible Perturbation Theory and Symmetric Integrators....Pages 375-390
Dissipatively Perturbed Hamiltonian and Reversible Systems....Pages 391-406
Highly Oscillatory Differential Equations....Pages 407-453
Dynamics of Multistep Methods....Pages 455-491
Back Matter....Pages 493-515

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Content:
Front Matter....Pages i-xiii
Examples and Numerical Experiments....Pages 1-22
Numerical Integrators....Pages 23-46
Order Conditions, Trees and B-Series....Pages 47-92
Conservation of First Integrals and Methods on Manifolds....Pages 93-130
Symmetric Integration and Reversibility....Pages 131-166
Symplectic Integration of Hamiltonian Systems....Pages 167-208
Further Topics in Structure Preservation....Pages 209-254
Structure-Preserving Implementation....Pages 255-286
Backward Error Analysis and Structure Preservation....Pages 287-326
Hamiltonian Perturbation Theory and Symplectic Integrators....Pages 327-374
Reversible Perturbation Theory and Symmetric Integrators....Pages 375-390
Dissipatively Perturbed Hamiltonian and Reversible Systems....Pages 391-406
Highly Oscillatory Differential Equations....Pages 407-453
Dynamics of Multistep Methods....Pages 455-491
Back Matter....Pages 493-515
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