Iterative Splitting Methods for Differential Equations

Juergen Geiser (Ernst-Moritz-Arndt University of Greifswald, Germany)

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English

Chapman & Hall/CRC
01 June 2011

Number systems; Algebra; Differential calculus & equations; Applied mathematics

Series: Chapman & Hall/CRC Numerical Analysis and Scientific Computing Series

Iterative Splitting Methods for Differential Equations explains how to solve evolution equations via novel iterative-based splitting methods that efficiently use computational and memory resources. It focuses on systems of parabolic and hyperbolic equations, including convection-diffusion-reaction equations, heat equations, and wave equations.

In the theoretical part of the book, the author discusses the main theorems and results of the stability and consistency analysis for ordinary differential equations. He then presents extensions of the iterative splitting methods to partial differential equations and spatial- and time-dependent differential equations. The practical part of the text applies the methods to benchmark and real-life problems, such as waste disposal, elastics wave propagation, and complex flow phenomena. The book also examines the benefits of equation decomposition. It concludes with a discussion on several useful software packages, including r3t and FIDOS.

Covering a wide range of theoretical and practical issues in multiphysics and multiscale problems, this book explores the benefits of using iterative splitting schemes to solve physical problems. It illustrates how iterative operator splitting methods are excellent decomposition methods for obtaining higher-order accuracy.

By: Juergen Geiser (Ernst-Moritz-Arndt University of Greifswald Germany)
Imprint: Chapman & Hall/CRC
Country of Publication: United States
Volume: 15
Dimensions: Height: 234mm, Width: 156mm,
Weight: 589g
ISBN: 9781439869826
ISBN 10: 1439869820
Series: Chapman & Hall/CRC Numerical Analysis and Scientific Computing Series
Pages: 328
Publication Date: 01 June 2011
Audience: College/higher education , General/trade , Primary , ELT Advanced
Format: Hardback
Publisher's Status: Active

Introduction. Model Problems. Iterative Decomposition of Ordinary Differential Equations. Decomposition Methods for Partial Differential Equations. Computation of the Iterative Splitting Methods: Algorithmic Part. Extensions of Iterative Splitting Schemes. Numerical Experiments. Summary and Perspectives. Software Tools. Appendix. Bibliography. Index.

Juergen Geiser is a researcher in the Department of Mathematics at the Humboldt-University of Berlin. His research interests include numerical and computational analysis, partial differential equations, decomposition and discretization methods for hyperbolic and parabolic equations, optimization, scientific computing, and interface analysis.