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

Varah, J. M.

doi:10.1090/S0025-5718-1972-0323087-4

On the solution of block-tridiagonal systems arising from certain finite-difference equations
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Math. Comp. 26 (1972), 859-868 Request permission

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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