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📚 Decomposition Methods for Differential Equations: Theory and Applications, H.
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eBay item number:184140618376
Item specifics
- Condition
- Subject
- Methods
- ISBN
- 9781439810965
- EAN
- 9781439810965
About this product
Product Identifiers
Publisher
CRC Press LLC
ISBN-10
1439810966
ISBN-13
9781439810965
eBay Product ID (ePID)
71759521
Product Key Features
Number of Pages
304 Pages
Publication Name
Decomposition Methods for Differential Equations : Theory and Applications
Language
English
Subject
Differential Equations / General, Operations Research, General, Applied
Publication Year
2009
Type
Textbook
Subject Area
Mathematics, Business & Economics
Series
Chapman and Hall/Crc Numerical Analysis and Scientific Computing Ser.
Format
Hardcover
Dimensions
Item Height
0.8 in
Item Weight
20 Oz
Item Length
9.5 in
Item Width
6.5 in
Additional Product Features
Intended Audience
College Audience
LCCN
2009-011786
Dewey Edition
22
Illustrated
Yes
Dewey Decimal
518/.6
Table Of Content
Preface Introduction Modeling: Multi-Physics Problems Introduction Models for Multi-Physics Problems Examples for Multi-Physics Problems Abstract Decomposition and Discretization Methods Decomposition Discretization Time-Decomposition Methods for Parabolic Equations Introduction for the Splitting Methods Iterative Operator-Splitting Methods for Bounded Operators Iterative Operator-Splitting Methods for Unbounded Operators Decomposition Methods for Hyperbolic Equations Introduction for the Splitting Methods ADI Methods and LOD Methods Iterative Operator-Splitting Methods for Wave Equations Parallelization of Time Decomposition Methods Nonlinear Iterative Operator-Splitting Methods Spatial Decomposition Methods Domain Decomposition Methods Based on Iterative Operator-Splitting Methods Schwarz Waveform-Relaxation Methods Overlapping Schwarz Waveform Relaxation for the Solution of Convection-Diffusion-Reaction Equation Numerical Experiments Introduction Benchmark Problems for the Time Decomposition Methods for Ordinary Differential and Parabolic Equations Benchmark Problems for Spatial Decomposition Methods: Schwarz Waveform-Relaxation Method Benchmark Problems: Hyperbolic Equations Real-Life Applications Summary and Perspectives Notation Appendix A: Software Tools Appendix B: Discretization Methods Literature References Index
Synopsis
Decomposition Methods for Differential Equations: Theory and Applications describes the analysis of numerical methods for evolution equations based on temporal and spatial decomposition methods. It covers real-life problems, the underlying decomposition and discretization, the stability and consistency analysis of the decomposition methods, and numerical results. The book focuses on the modeling of selected multi-physics problems, before introducing decomposition analysis. It presents time and space discretization, temporal decomposition, and the combination of time and spatial decomposition methods for parabolic and hyperbolic equations. The author then applies these methods to numerical problems, including test examples and real-world problems in physical and engineering applications. For the computational results, he uses various software tools, such as MATLAB®, R3T, WIAS-HiTNIHS, and OPERA-SPLITT. Exploring iterative operator-splitting methods, this book shows how to use higher-order discretization methods to solve differential equations. It discusses decomposition methods and their effectiveness, combination possibility with discretization methods, multi-scaling possibilities, and stability to initial and boundary values problems., Decomposition Methods for Differential Equations: Theory and Applications describes the analysis of numerical methods for evolution equations based on temporal and spatial decomposition methods. It covers real-life problems, the underlying decomposition and discretization, the stability and consistency analysis of the decomposition methods, and numerical results. The book focuses on the modeling of selected multi-physics problems, before introducing decomposition analysis. It presents time and space discretization, temporal decomposition, and the combination of time and spatial decomposition methods for parabolic and hyperbolic equations. The author then applies these methods to numerical problems, including test examples and real-world problems in physical and engineering applications. For the computational results, he uses various software tools, such as MATLAB(R), R3T , WIAS-HiTNIHS, and OPERA-SPLITT . Exploring iterative operator-splitting methods, this book shows how to use higher-order discretization methods to solve differential equations. It discusses decomposition methods and their effectiveness, combination possibility with discretization methods, multi-scaling possibilities, and stability to initial and boundary values problems., Exploring iterative operator-splitting methods, this work describes the analysis of numerical methods for evolution equations based on temporal and spatial decomposition methods. It generalizes the numerical analysis with respect to the consistency and stability to nonlinear, stiff, and spatial decomposed splitting problems. The book focuses on parabolic and hyperbolic equations, including convection-diffusion-reaction, heat, and wave equations, and applies the results to computational science issues, such as flow problems, elastic-wave propagation, heat transfer, and micromagnetic problems. Software tools are listed in an appendix.
LC Classification Number
QA402.2.G45 2009
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