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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."
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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