A concise introduction to geometric numerical integration. (2016)

• Record Type: Book
• Further Information: Note: Sergio Blanes, Fernando Casas.
• Authors: Blanes, Sergio; Casas, Fernando
• Contents: What is geometric numerical integration?; First elementary examples and numerical methods; Classical paradigm of numerical integration; Towards a new paradigm: geometric numerical integration; Symplectic integration; Illustration: the Kepler problem; What is to be treated in this book (and what is not) Classical integrators and preservation of properties ; Taylor series methods; Runge–Kutta methods; Multistep methods; Numerical examples Splitting and composition methods ; Introduction; Composition and splitting; Order conditions of splitting and composition methods; Splitting methods for special systems; Processing; Splitting methods for non-autonomous systems; A collection of low order splitting and composition methods; Illustrations Other types of geometric numerical integrators ; Symplectic methods based on generating functions; Variational integrators; Volume-preserving methods; Lie group methods Long-time behavior of geometric integrators ; Introduction. Examples; Modified equations; Modified equations of splitting and composition methods; Estimates over long-time intervals; Application: extrapolation methods Time-splitting methods for PDEs of evolution ; Introduction; Splitting methods for the time-dependent Schrödinger equation; Splitting methods for parabolic evolution equations Appendix: Some additional mathematical results Bibliography Index Exercises appear at the end of each chapter.
• Edition: 1st
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2016
• Extent: 1 online resource
• Subjects: 515.352; Differential equations -- Numerical solutions; Numerical integration; Hamiltonian systems
• Languages: English
• ISBNs: 9781482263442
• Notes: Note: Description based on CIP data; resource not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
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