| Description |
1 online resource (xi, 376 pages) : illustrations |
| Series |
Chapman & Hall/CRC numerical analysis and scientific computing |
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Chapman & Hall/CRC numerical analysis and scientific computing
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| Contents |
1. Introduction and summary of this book An introductory example: the spinodal decomposition -- History -- Derivation of dissipative or conservative schemes advanced topics -- 2. Target partial differential equations -- Variational derivatives -- First-order real-valued PDEs -- First-order complex-valued PDEs -- Systems of first-order PDEs -- Second-order PDEs -- 3. Discrete variational derivative method -- Discrete symbols and formulas -- Procedure for first-order real-valued PDEs -- Procedure for first-order complex-valued PDEs -- Procedure for systems of first-order PDEs -- Procedure for second-order PDEs -- Preliminaries on discrete functional analysis -- 4. Applications -- Target PDEs 1 -- Target PDEs 2 -- Target PDEs 3 -- Target PDEs 4 -- Target PDEs 5 -- Target PDEs 7 -- Other equations -- 5. Advanced topic I: design of high-order schemes -- Orders of accuracy of schemes -- Spatially high-order schemes -- Temporally high-order schemes: composition method -- Temporally high-order schemes: high-order discrete variational derivatives -- 6. Advanced topic II: design of linearly-implicit schemes -- Basic idea for constructing linearly-implicit schemes -- Multiple-points discrete variational derivative -- Design of schemes -- Applications -- Remarks on the stability of linearly-implicit schemes -- 7. Advanced topic III: further remarks -- Solving system of nonlinear equations -- Switch to Galerkin framework -- Extension to non-rectangular meshes on 2D Region -- A. Semi-discrete schemes in space B -- Proof of Proposition 3.4 |
| Summary |
"Many important problems in engineering and science are modeled by nonlinear partial differential equations (PDEs). A new trend in PDEs, called structure-preserving numerical methods, has recently developed. This book is devoted to one such technique, called the discrete variational derivative method. First, the text introduces the key factors and the basic ideas of this method, followed by target problems solvable by the method. The second section describes the rigorous mathematics in detail along with relevant applications, which are illustrated by worked examples. It concludes with a comprehensive of listing of essential references on structure-preserving algorithms for advanced readers"-- Provided by publisher |
| Bibliography |
Includes bibliographical references and index |
| Notes |
English |
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Print version record |
| Subject |
Differential equations, Partial -- Numerical solutions.
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Nonlinear theories.
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Engineering mathematics.
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MATHEMATICS -- Numerical Analysis.
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Differential equations, Partial -- Numerical solutions
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Engineering mathematics
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Nonlinear theories
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| Form |
Electronic book
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| Author |
Matsuo, Takayasu
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| ISBN |
9781420094466 |
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1420094467 |
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0429148461 |
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9780429148460 |
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