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A First Course in the Numerical Analysis of Differential Equations

2nd Edition



Part of Cambridge Texts in Applied Mathematics

  • Date Published: December 2008
  • availability: In stock
  • format: Paperback
  • isbn: 9780521734905


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About the Authors
  • 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 new 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.

    • No other book covers this range of subjects.
    • A valuable introductory text for mathematicians, scientists, engineers and computer scientists, featuring copious illustrations and structured exercises
    • The author's clear and lively style make this rigorous text an enjoyable read
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    Product details

    • Edition: 2nd Edition
    • Date Published: December 2008
    • format: Paperback
    • isbn: 9780521734905
    • length: 477 pages
    • dimensions: 248 x 174 x 24 mm
    • weight: 0.84kg
    • contains: 4 b/w illus. 163 exercises
    • availability: In stock
  • 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

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  • Author

    Arieh Iserles, University of Cambridge
    Arieh Iserles is a Professor in Numerical Analysis of Differential Equations in the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge. He has been awarded the Onsager medal and served as a chair of the Society for Foundations of Computational Mathematics. He is also Managing Editor of Acta Numerica, Editor in Chief of Foundations of Computational Mathematics, and an editor of numerous other publications.

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