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Strang-type preconditioners for systems of LMF-based ODE codes
Chan R.H.1; Ng M.K.1; Jin X.-Q.2
2001-04-01
Source PublicationIMA Journal of Numerical Analysis
ISSN02724979
Volume21Issue:2Pages:451-462
Abstract

We consider the solution of ordinary differential equations (ODEs) using boundary value methods. These methods require the solution of one or more unsymmetric, large and sparse linear systems. The GMRES method with the Strang-type block-circulant preconditioner is proposed for solving these linear systems. We show that if an A-stable boundary value method is used for an m-by-m system of ODEs, then our preconditioners are invertible and all the eigenvalues of the preconditioned systems are 1 except for at most 2m(k + k) outliers. It follows that when the GMRES method is applied to solving the preconditioned systems, the method will converge in at most 2m(k + k) + 1 iterations. Numerical results are given to illustrate the effectiveness of our methods.

KeywordBoundary-value Methods Stability Iteration
DOI10.1093/imanum/21.2.451
URLView the original
Indexed BySCI
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000168263700001
PublisherOXFORD UNIV PRESS
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Citation statistics
Cited Times [WOS]:35   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Affiliation1.Department of Mathematics, The Chinese University of Hong Kong,Shatin,HongKong
2.Faculty of Science and Technology, University of Macau,Macau
Recommended Citation
GB/T 7714
Chan R.H.,Ng M.K.,Jin X.-Q.. Strang-type preconditioners for systems of LMF-based ODE codes[J]. IMA Journal of Numerical Analysis,2001,21(2):451-462.
APA Chan R.H.,Ng M.K.,&Jin X.-Q..(2001).Strang-type preconditioners for systems of LMF-based ODE codes.IMA Journal of Numerical Analysis,21(2),451-462.
MLA Chan R.H.,et al."Strang-type preconditioners for systems of LMF-based ODE codes".IMA Journal of Numerical Analysis 21.2(2001):451-462.
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