A First Course in the Numerical Analysis of Differential Equations Cambridge Texts in Applied Mathematics, Series Number 44 2nd Edition by Arieh Iserles ISBN 0521734908 978-0521734905

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Product details: 

ISBN 10: 0521734908

ISBN 13: 978-0521734905

Author: Arieh Iserles 

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: 

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

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Arieh Iserles,Numerical Analysis,Equations Cambridge,Applied Mathematics