A first course in the numerical analysis of differential equations
著者
書誌事項
A first course in the numerical analysis of differential equations
(Cambridge texts in applied mathematics)
Cambridge University Press, 2009
2nd ed
- : pbk
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注記
Includes bibliographical reference and index
内容説明・目次
内容説明
Numerical analysis presents different faces to the world. For mathematicians it is a bona fide mathematical theory with an applicable flavour. For scientists and engineers it is a practical, applied subject, part of the standard repertoire of modelling techniques. For computer scientists it is a theory on the interplay of computer architecture and algorithms for real-number calculations. The tension between these standpoints is the driving force of this book, which presents a rigorous account of the fundamentals of numerical analysis of both ordinary and partial differential equations. The exposition maintains a balance between theoretical, algorithmic and applied aspects. This second edition has been extensively updated, and includes new chapters on emerging subject areas: geometric numerical integration, spectral methods and conjugate gradients. Other topics covered include multistep and Runge-Kutta methods; finite difference and finite elements techniques for the Poisson equation; and a variety of algorithms to solve large, sparse algebraic systems.
目次
- Preface to the first edition
- Preface to the second edition
- Flowchart of contents
- Part I. Ordinary Differential Equations: 1. Euler's method and beyond
- 2. Multistep methods
- 3. Runge-Kutta methods
- 4. Stiff equations
- 5. Geometric numerical integration
- 6. Error control
- 7. Nonlinear algebraic systems
- Part II. The Poisson Equation: 8. Finite difference schemes
- 9. The finite element method
- 10. Spectral methods
- 11. Gaussian elimination for sparse linear equations
- 12. Classical iterative methods for sparse linear equations
- 13. Multigrid techniques
- 14. Conjugate gradients
- 15. Fast Poisson solvers
- Part III. Partial Differential Equations of evolution: 16. The diffusion equation
- 17. Hyperbolic equations
- Appendix. Bluffer's guide to useful mathematics: A.1. Linear algebra
- A.2. Analysis
- Bibliography
- Index.
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