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

Arieh Iserles

（Cambridge texts in applied mathematics）

Cambridge University Press, 2009

2nd ed

  • : pbk

大学図書館所蔵 件 / 全13件

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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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