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基本説明
A new type of graduate textbook, comprising print, and interactive electronic components (on CD).
Full Description
Numerical Solution of Hyperbolic Partial Differential Equations is a new type of graduate textbook, with both print and interactive electronic components (on CD). It is a comprehensive presentation of modern shock-capturing methods, including both finite volume and finite element methods, covering the theory of hyperbolic conservation laws and the theory of the numerical methods. The range of applications is broad enough to engage most engineering disciplines and many areas of applied mathematics. Classical techniques for judging the qualitative performance of the schemes are used to motivate the development of classical higher-order methods. The interactive CD gives access to the computer code used to create all of the text's figures, and lets readers run simulations, choosing their own input parameters; the CD displays the results of the experiments as movies. Consequently, students can gain an appreciation for both the dynamics of the problem application, and the growth of numerical errors.
Contents
Preface; 1. Introduction to partial differential equations; 2. Scalar hyperbolic conservations laws; 3. Nonlinear scalar laws; 4, Nonlinear hyperbolic systems; 5. Methods for scalar laws; 6. Methods for hyperbolic systems; 7. Methods in multiple dimensions; 8. Adaptive mesh refinement; Bibliography; Index.
