On the Solution of Block-Tridiagonal Systems Arising from Certain Finite-Difference Equations

J. M. Varah
1972 Mathematics of Computation  
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
more » ... he 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.
doi:10.2307/2005868 fatcat:y24k67a5cjc3vje6augivsz4ne