Explicit solution of block tridiagonal systems of linear equations
Information Processing Letters
Round-Off Error in the Numerical Solution of the Heat Equation
Journal of the ACM (JACM)
An algorithm for solving a special class of tridiagonal systems of linear equations
Communications of the ACM
A cyclic block-tridiagonal solver
Advances in Engineering Software
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part I: ICCS 2007
A cyclic block-tridiagonal solver
Advances in Engineering Software
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The popular sequential Thomas algorithm for the numerical solution of tridiagonal linear algebraic equation systems is extended on a class of quasi-block-tridiagonal equation systems arising from finite-difference discretisations of boundary value and initial boundary value problems of reaction-migration-advection-diffusion type in one space dimension, occuring in electrochemistry. The extension allows for a simultaneous consideration of: (a) multiple space intervals with common boundaries; (b) additional algebraic or differential-algebraic equations coupled with mixed boundary conditions, that may express e.g. adsorption at the boundaries; (c) three-point finite-difference approximations to the gradients of the solutions of the initial/boundary value problems at the boundaries; (d) periodic or non-periodic boundary conditions at the external boundaries. The resulting equation matrix may include nonzero off-diagonal corner blocks associated with periodic boundary conditions, may be locally block-pentadiagonal at a number of isolated rows corresponding to internal spatial boundaries, and its blocks may have variable dimensions. Testing calculations are performed.