Finite difference schemes and partial differential equations
著者
書誌事項
Finite difference schemes and partial differential equations
Chapman & Hall, c1989
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注記
Bibliography: p. 379-382
Includes index
内容説明・目次
内容説明
This book combines practical aspects of implementation with theoretical analysis of finite difference schemes and partial differences schemes. There is a thorough discussion of the concepts of convergence, consistency, and stability for time-dependent equations. The von Neumann analysis of stability is developed rigorously using the methods of Fourier analysis. Fourier analysis is used throughout the text, providing a unified treatment of the basic concepts and results. A complete proof of the Lax-Richtmyer theorem for equations with constant coefficients is included.
目次
Hyperbolic partial differential equations and finite difference schemes. Analysis of finite difference schemes. Accuracy of finite difference schemes. Multistep finite difference schemes. Dissipation and dispersion. Parabolic partial differential equations in higher dimensions. Second-order equations. Analysis of well-posed and stable problems. Convergence estimates for initial value problems. Initial boundary value problems. Elliptic partial differential equations. Linear iterative methods. The method of steepest descent and the conjugate gradient methods.
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