Computing periodic solutions of linear differential-algebraic equations by waveform relaxation |
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Authors: | Yao-Lin Jiang Richard M. M. Chen. |
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Affiliation: | Department of Mathematical Sciences, Xi'an Jiaotong University, Xi'an, People's Republic of China ; School of Creative Media, City University of Hong Kong, Hong Kong, People's Republic of China |
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Abstract: | We propose an algorithm, which is based on the waveform relaxation (WR) approach, to compute the periodic solutions of a linear system described by differential-algebraic equations. For this kind of two-point boundary problems, we derive an analytic expression of the spectral set for the periodic WR operator. We show that the periodic WR algorithm is convergent if the supremum value of the spectral radii for a series of matrices derived from the system is less than 1. Numerical examples, where discrete waveforms are computed with a backward-difference formula, further illustrate the correctness of the theoretical work in this paper. |
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Keywords: | Differential-algebraic equations periodic solutions waveform relaxation spectra of linear operators linear multistep methods finite-difference numerical analysis scientific computing circuit simulation |
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