2nd ed. - Cambridge, UK ; New York : Cambridge University Press, 2009.
xviii, 459 p. : ill. ; 25 cm.
Numerical analysis of differential equations
Includes bibliographical references and index.
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.
(source: Nielsen Book Data)
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. (source: Nielsen Book Data)