Numerical Methods for Grid Equations: Volume I Direct Methods

✍ Scribed by Aleksandr A. Samarskii, Evgenii S. Nikolaev (auth.)

• Publisher: Birkhäuser Basel
• Year: 1989
• Tongue: English
• Leaves: 272
• Edition: 1
• Category: Library

✦ Synopsis

The finite-difference solution of mathematical-physics differential equations is carried out in two stages: 1) the writing of the difference scheme (a differ­ ence approximation to the differential equation on a grid), 2) the computer solution of the difference equations, which are written in the form of a high­ order system of linear algebraic equations of special form (ill-conditioned, band-structured). Application of general linear algebra methods is not always appropriate for such systems because of the need to store a large volume of information, as well as because of the large amount of work required by these methods. For the solution of difference equations, special methods have been developed which, in one way or another, take into account special features of the problem, and which allow the solution to be found using less work than via the general methods. This work is an extension of the book Difference M ethod3 for the Solution of Elliptic Equation3 by A. A. Samarskii and V. B. Andreev which considered a whole set of questions connected with difference approximations, the con­ struction of difference operators, and estimation of the ~onvergence rate of difference schemes for typical elliptic boundary-value problems. Here we consider only solution methods for difference equations. The book in fact consists of two volumes.

✦ Table of Contents

Front Matter....Pages i-xxxv
Direct Methods for Solving Difference Equations....Pages 1-59
The Elimination Method....Pages 61-116
The Cyclic Reduction Method....Pages 117-170
The Separation of Variables Method....Pages 171-238
Back Matter....Pages 239-242

✦ Subjects

Computational Mathematics and Numerical Analysis