A First Course in the Numerical Analysis of Differential Equations
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A First Course in the Numerical Analysis of Differential Equations: (Series Number 44 Cambridge Texts in Applied Mathematics)

A First Course in the Numerical Analysis of Differential Equations: (Series Number 44 Cambridge Texts in Applied Mathematics)

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About the Book

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.

Table of Contents:
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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Product Details
  • ISBN-13: 9780521734905
  • Publisher: Cambridge University Press
  • Publisher Imprint: Cambridge University Press
  • Edition: Revised edition
  • Language: English
  • Returnable: N
  • Returnable: N
  • Spine Width: 25 mm
  • Width: 175 mm
  • ISBN-10: 0521734908
  • Publisher Date: 27 Nov 2008
  • Binding: Paperback
  • Height: 244 mm
  • No of Pages: 480
  • Returnable: N
  • Series Title: Series Number 44 Cambridge Texts in Applied Mathematics
  • Weight: 807 gr


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A First Course in the Numerical Analysis of Differential Equations: (Series Number 44 Cambridge Texts in Applied Mathematics)
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