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Strang-type preconditioners for solving linear systems from delay differential equations
Lin F.R.1; Jin X.Q.2; Lei S.L.2,3
2003-03-01
Source PublicationBIT Numerical Mathematics
ISSN00063835
Volume43Issue:1Pages:139-152
Abstract

We consider the solution of delay differential equations (DDEs) by using boundary value methods (BVMs). These methods require the solution of one or more nonsymmetric, 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 a Pk,k-stable BVM is used for solving an m-by-m system of DDEs, then our preconditioner is invertible and all the eigenvalues of the preconditioned system are clustered around 1. It follows that when the GMRES method is applied to solving the preconditioned systems, the method may converge fast. Numerical results are given to illustrate the effectiveness of our methods.

KeywordBlock-circulant Pre-conditioner Boundary Value Method Delay Differential Equation Gmres Method
DOI10.1023/A:1023657107334
URLView the original
Indexed BySCI
WOS Research AreaComputer Science ; Mathematics
WOS SubjectComputer Science, Software Engineering ; Mathematics, Applied
WOS IDWOS:000182583300010
PublisherKLUWER ACADEMIC PUBL
Fulltext Access
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Cited Times [WOS]:13   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Affiliation1.Department of Mathematics, Shantou University, Shantou, Guangdong 515063, China
2.Faculty of Science and Technology, University of Macau, Macau, China
3.Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong, China
Recommended Citation
GB/T 7714
Lin F.R.,Jin X.Q.,Lei S.L.. Strang-type preconditioners for solving linear systems from delay differential equations[J]. BIT Numerical Mathematics,2003,43(1):139-152.
APA Lin F.R.,Jin X.Q.,&Lei S.L..(2003).Strang-type preconditioners for solving linear systems from delay differential equations.BIT Numerical Mathematics,43(1),139-152.
MLA Lin F.R.,et al."Strang-type preconditioners for solving linear systems from delay differential equations".BIT Numerical Mathematics 43.1(2003):139-152.
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