Paper Info
Title
Algorithms for Almost Block Diagonal Linear Systems.
Abstract
Codes for solving systems of ordinary differential equations for use in the method of lines for partial differential equations (PDEs) usually provide only a banded system solver. In this context, a frequently occurring structure is almost block diagonal (ABD). Solving ABD systems by imposing banded structure introduces fill-in and is inefficient. Though robust, efficient ABD software has been developed and used in packages for solving boundary value problems with separated boundary conditions for ordinary differential equations (BVODEs), it has not been generally exploited in PDE software. The situation with bordered almost block diagonal system software for BVODEs with nonseparated boundary conditions is less satisfactory. This survey draws on material from a variety of sources, particularly [P. Armodio et al., Numer. Linear Algebra Appl., 7 (2000), pp. 275-317] and [B. Garrett and I. Gladwell, J. Comput. Methods Sci. Engrg., 1 (2001), pp. 75-98] and the references therein.
Year
DOI
Venue
2004
10.1137/S003614450240506X
SIAM REVIEW
Keywords
Field
DocType
almost block diagonal systems,direct algorithms,boundary value problems for ordinary,differential equations,method of lines
Linear algebra,Differential equation,Boundary value problem,Ordinary differential equation,Linear system,Mathematical analysis,Method of lines,Partial differential equation,Block matrix,Mathematics
Journal
Volume
Issue
ISSN
46
1
0036-1445
Citations 
PageRank 
References 
11
0.86
0
Authors
2
Name
Order
Citations
PageRank
Graeme Fairweather114233.42
Ian Gladwell26612.63