Numerical Methods for Grid Equations Volume I Direct Methods
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 fo...
| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
Basel
Birkhäuser
1989, 1989
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| Edition: | 1st ed. 1989 |
| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 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