Author | Samarskii, Aleksandr A. author |
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Title | Numerical Methods for Grid Equations [electronic resource] : Volume I Direct Methods / by Aleksandr A. Samarskii, Evgenii S. Nikolaev |
Imprint | Basel : Birkhรคuser Basel, 1989 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-9272-8 |
Descript | XXXV, 242 p. online resource |
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