Difference Methods for Initial-Value Problems
ISBN/ASIN: 0894647636,9780894647635 | 1967 | English | djvu | 419/419 pages | 7.75 Mb
Publisher: Interscience Publishers | Author: Robert D. Richtmyer, K. W. Morton | Edition: Second
This is the second edition of a book, first published in 1957, and is divided into two parts: the first contains the theory of difference methods and the second, applications of this theory.
Part 1 starts with a chapter in which the heat flow problem in its simplest form is treated. This is most appropriate because it makes it possible to introduce many of the important concepts and methods of the theory of difference approximations in a simple but still instructive way. Then finite-difference methods for general initial-value problems are introduced and the relations among stability, consistency and convergence are made clear.
The remaining chapters of Part 1 are devoted to specific classes of problems, beginning with constant coefficient problems and proceeding to more difficult cases: variable coefficient and nonlinear problems and mixed initial-boundary value problems. The most important results obtained after 1957 are included in this second edition. A merit of the book is that some of the proofs are simplifications of the original ones.
As already mentioned, the second part contains applications. Where the stability theory developed in Part 1 is inadequate (because it only concerns the behavior in the limit Δt→0), the book provides practical stability criteria.
All chapters of the book have been considerably revised since the first edition. There are three entirely new chapters: one concerning mixed initial-boundary value problems and one in Part 2 called Multi-dimensional-fluid dynamics.
The book is primarily written for users of difference methods, but it can be highly recommended to everyone interested in the subject.