A first course in the numerical analysis of differential equations. 2nd ed. (English) Zbl 1171.65060

Iserles, Arieh

Cambridge Texts in Applied Mathematics. Cambridge: Cambridge University Press (ISBN 978-0-521-73490-5/pbk). xix, 459 p. (2009).

The new chapters are written in the same spirit as in the first edition of the book (1995; Zbl 0841.65001). The author concentrates on the fundamentals in deriving methods from basic principles and analyses them with a variety of mathematical techniques. The second and third new chapter provide important topics in integrating partial differential equations while the first one takes up developements during the last years in searching methods which conserve qualitative features, e.g. when dealing with Hamiltonian systems.
The present book can, because of the extension even more than the first edition, be highly recommended for readers from all fields, including students and engineers.

Reviewer: Rolf Dieter Grigorieff (Berlin)

MSC:

65Mxx	Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis
65Lxx	Numerical methods for ordinary differential equations
65Nxx	Numerical methods for partial differential equations, boundary value problems
65F05	Direct numerical methods for linear systems and matrix inversion
65F10	Iterative numerical methods for linear systems
65H10	Numerical computation of solutions to systems of equations

Keywords:

textbook; Runge-Kutta methods; multistep methods; stiff equations; geometrical numerical integration; error control; Poisson equation; finite difference method; finite element method; spectral methods; Gaussian elimination; iterative methods; multigrid techniques; conjugate gradients; fast Poisson solvers; diffusion equation; hyperbolic equations; Hamiltonian systems