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Field name	Details
Dewey Class	518
Title	Numerical Methods for Grid Equations ([EBook]) : Volume I Direct Methods / by Aleksandr A. Samarskii, Evgenii S. Nikolaev.
Author	Samarskii, Aleksandr A.
Added Personal Name	Nikolaev, Evgenii S.
Other name(s)	SpringerLink (Online service)
Publication	Basel : Birkhäuser , 1989.
Physical Details	XXXV, 242 pages : online resource.
ISBN	9783034892728
Summary Note	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.:
Contents note	1 Direct Methods for Solving Difference Equations -- 1.1 Grid equations. Basic concepts -- 1.2 The general theory of linear difference equations -- 1.3 The solution of linear equations with constant coefficients -- 1.4 Second-order equations with constant coefficients -- 1.5 Eigenvalue difference problems -- 2 The Elimination Method -- 2.1 The elimination method for three-point equations -- 2.2 Variants of the elimination method -- 2.3 The elimination method for five-point equations -- 2.4 The block-elimination method -- 3 The Cyclic Reduction Method -- 3.1 Boundary-value problems for three-point vector equations -- 3.2 The cylic reduction method for a boundary-value problem of the first kind -- 3.3 Sample applications of the method -- 3.4 The cyclic reduction method for other boundary-value problems -- 4 The Separation of Variables Method -- 4.1 The algorithm for the discrete Fourier transform -- 4.2 The solution of difference problems by the Fourier method -- 4.3 The method of incomplete reduction -- 4.4 The staircase algorithm and the reduction method for solving tridiagonal systems of equations.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-0348-9272-8
Links to Related Works	Subject References: Computational Mathematics and Numerical Analysis . Computer mathematics . Mathematics . Authors: author . Nikolaev, Evgenii S. . Samarskii, Aleksandr A. . See Also: Samarskij, Aleksandr A., 1919- . Corporate Authors: SpringerLink (Online service) . Classification: 518 .

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Numerical Methods for Grid Equations: Volume I Direct Methods

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