Strang‐type preconditioners applied to ordinary and neutral differential‐algebraic equations |
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Authors: | Chengjian Zhang Hao Chen Leiming Wang |
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Institution: | School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan People's Republic of 430074, China |
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Abstract: | This paper deals with boundary‐value methods (BVMs) for ordinary and neutral differential‐algebraic equations. Different from what has been done in Lei and Jin (Lecture Notes in Computer Science, vol. 1988. Springer: Berlin, 2001; 505–512), here, we directly use BVMs to discretize the equations. The discretization will lead to a nonsymmetric large‐sparse linear system, which can be solved by the GMRES method. In order to accelerate the convergence rate of GMRES method, two Strang‐type block‐circulant preconditioners are suggested: one is for ordinary differential‐algebraic equations (ODAEs), and the other is for neutral differential‐algebraic equations (NDAEs). Under some suitable conditions, it is shown that the preconditioners are invertible, the spectra of the preconditioned systems are clustered, and the solution of iteration converges very rapidly. The numerical experiments further illustrate the effectiveness of the methods. Copyright © 2011 John Wiley & Sons, Ltd. |
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Keywords: | ordinary and neutral differential‐algebraic equations linear systems Strang‐type precon‐ditioner boundary‐value methods convergence rate |
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