Numerical solution of differential equations : introduction to finite difference and finite element methods
著者
書誌事項
Numerical solution of differential equations : introduction to finite difference and finite element methods
Cambridge University Press, 2018
- : hardback
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注記
Includes bibliographical references (p. 289-290) and index
内容説明・目次
内容説明
This introduction to finite difference and finite element methods is aimed at graduate students who need to solve differential equations. The prerequisites are few (basic calculus, linear algebra, and ODEs) and so the book will be accessible and useful to readers from a range of disciplines across science and engineering. Part I begins with finite difference methods. Finite element methods are then introduced in Part II. In each part, the authors begin with a comprehensive discussion of one-dimensional problems, before proceeding to consider two or higher dimensions. An emphasis is placed on numerical algorithms, related mathematical theory, and essential details in the implementation, while some useful packages are also introduced. The authors also provide well-tested MATLAB (R) codes, all available online.
目次
- 1. Introduction
- Part I. Finite Difference Methods: 2. Finite difference methods for 1D boundary value problems
- 3. Finite difference methods for 2D elliptic PDEs
- 4. FD methods for parabolic PDEs
- 5. Finite difference methods for hyperbolic PDEs
- Part II. Finite Element Methods: 6. Finite element methods for 1D boundary value problems
- 7. Theoretical foundations of the finite element method
- 8. Issues of the FE method in one space dimension
- 9. The finite element method for 2D elliptic PDEs
- Appendix. Numerical solutions of initial value problems
- References
- Index.
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