On convergence conditions of waveform relaxation methods for linear differential-algebraic equations

Authors:
Zhong-Zhi Bai;Xi Yang
Affiliations:
School of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, PR China and State Key Laboratory of Scientific/Engineering Computing, Institute of Computational Mathematics ...;State Key Laboratory of Scientific/Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy o ...
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

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Abstract

For linear constant-coefficient differential-algebraic equations, we study the waveform relaxation methods without demanding the boundedness of the solutions based on infinite time interval. In particular, we derive explicit expression and obtain asymptotic convergence rate of this class of iteration schemes under weaker assumptions, which may have wider and more useful application extent. Numerical simulations demonstrate the validity of the theory.