About this Physics and Astronomy article

Computational methods in ordinary differential equations: J.D. Lambert (John Wiley, 1972), £5.50 by D.F. Mayers is a Physics and Astronomy article available to read on EtoBox.

Here is a book which should appeal to both the theoretical numerical analyst and the practical mathematician with problems which require numerical solution. It contains no programs, and few formal proofs of mathematical theorems, but it is "intended to cast light (and in some cases doubt) on our interpretation of why numerical methods perform in the way that they do". The book is almost entirely devoted to initial-value problems; a very brief appendix deals with shooting methods for boundary-value problems, which are of course very different in nature. It deals extensively with linear multi-step methods, and with Runge-Kutta processes, but without mentioning other special methods, such as the use of Chebyshev polynomials, series expansions, and collocation methods. There is a strong emphasis on the basic analysis for a single first-order equation. The practical problems which arise when implementing an implicit method for a large system of simultaneous equations are given less prominence. The different ways in which rounding errors are propagated in different methods are scarcely mentioned. Within these limitations the treatment is excellent, and Dr. Lambert gives a very full discu

Author

D.F. Mayers

Publisher

Elsevier Science; Elsevier ; Elsevier BV (ISSN 0010-4655)

Published

1974

Language

EN

Field

Physics and Astronomy (Physical Sciences)