Solving Bordered Almost Block Diagonal Linear Systems Stably and Efficiently

Article type: Research Article

Authors: Garrett, B. | Gladwell, I.

Affiliations: Department of Mathematics, Southern Methodist University, Dallas, TX 75275, USA

Abstract: Almost block diagonal (ABD) linear systems arise in a variety of contexts, specifically in the numerical solution of systems of ordinary differential equation two-point boundary value problems with separated boundary conditions. The stable, efficient solution of ABDs has received much attention recently. Bordered almost block diagonal (BABD) linear systems arise when the boundary conditions are non-separated. After an introduction to the problem, we describe a variety of direct approaches to solving BABD systems, some of them extensions of ABD techniques. We pay particular attention to questions of efficiency and stability.

Keywords: Bordered almost block diagonal systems, direct algorithms, boundary value problems

DOI: 10.3233/JCM-2001-1102

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 1, no. 1, pp. 75-97, 2001