Computing periodic solutions of linear differential-algebraic equations by waveform relaxation
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- by Yao-Lin Jiang and Richard M. M. Chen PDF
- Math. Comp. 74 (2005), 781-804 Request permission
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.References
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Additional Information
- Yao-Lin Jiang
- Affiliation: Department of Mathematical Sciences, Xi’an Jiaotong University, Xi’an, People’s Republic of China
- Email: yljiang@mail.xjtu.edu.cn
- Richard M. M. Chen
- Affiliation: School of Creative Media, City University of Hong Kong, Hong Kong, People’s Republic of China
- Email: richard.chen@cityu.edu.hk
- Received by editor(s): June 5, 2002
- Received by editor(s) in revised form: August 25, 2003
- Published electronically: July 20, 2004
- © Copyright 2004 American Mathematical Society
- Journal: Math. Comp. 74 (2005), 781-804
- MSC (2000): Primary 37M05, 65F10, 65L10, 65L80, 65Y05
- DOI: https://doi.org/10.1090/S0025-5718-04-01665-5
- MathSciNet review: 2114648