Numerical Methods for Grid Equations

E. S. Nikolaev

ISBN 10: 3034899726 / ISBN 13: 9783034899727

Published by Birkhäuser Basel Nov 2011, 2011

About this Item

This item is printed on demand - it takes 3-4 days longer - Neuware -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. 284 pp. Englisch.

Seller Inventory # 9783034899727

Bibliographic Details

• Title: Numerical Methods for Grid Equations
• Publisher: Birkhäuser Basel Nov 2011
• Publication Date: 2011
• Language: English
• ISBN 10: 3034899726
• ISBN 13: 9783034899727
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 254W x 178H x 16D millimeters 254 millimeters width by 178 millimeters height by 16 millimeters depth
• Weight: 540 grams

About this title

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.