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Table of contents (4 chapters)
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About this book
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.
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Bibliographic Information
Book Title: Numerical Methods for Grid Equations
Book Subtitle: Volume I Direct Methods
Authors: Aleksandr A. Samarskii, Evgenii S. Nikolaev
DOI: https://doi.org/10.1007/978-3-0348-9272-8
Publisher: Birkhäuser Basel
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eBook Packages: Springer Book Archive
Copyright Information: Birkhäuser Verlag Basel 1989
Hardcover ISBN: 978-3-7643-2276-2Published: 01 December 1988
Softcover ISBN: 978-3-0348-9972-7Published: 03 November 2011
eBook ISBN: 978-3-0348-9272-8Published: 06 December 2012
Edition Number: 1
Number of Pages: XXXV, 242