Strang-Type Preconditioners for Solving Linear Systems from Delay Differential Equations |
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| Authors: | F R Lin X Q Jin S L Lei |
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| Institution: | (1) 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;(4) Faculty of Science and Technology, University of Macau, Macau, China |
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| 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 P
k
1,k
2-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. |
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| Keywords: | Delay differential equation boundary value method block-circulant preconditioner GMRES method |
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