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Mathematics of Computation

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On the solution of block-tridiagonal systems arising from certain finite-difference equations

Author: J. M. Varah
Journal: Math. Comp. 26 (1972), 859-868
MSC: Primary 65F05
MathSciNet review: 0323087
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Abstract: We consider the solution of the linear systems arising from certain implicit finite-difference approximations to systems of linear differential equations. In particular, we consider those schemes which lead to matrices of block-tridiagonal form. There are two common methods for solving such equations: using a block-tridiagonal factorization (blocksolve), or treating the matrix as a band matrix (bandsolve).

First, we discuss conditions for ensuring the numerical stability of the block-tridiagonal factorization for general matrices of this form. Then, we compare the two methods for general block-tridiagonal matrices (including matrices arising from the Crank-Nicolson scheme for systems of parabolic equations) and for a more specialized block-tridiagonal matrix which arises from schemes of H. B. Keller for systems of two-point boundary value problems and parabolic equations.

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Keywords: Solution of difference equations, band matrices, block-tridiagonal matrices
Article copyright: © Copyright 1972 American Mathematical Society