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

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摘要

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.

论文关键词:44A10,65L05,65L20,65L80,65N15,CR: G1.3,Differential-algebraic equations,Laplace transform,Waveform relaxation method,Convergence theory

论文评审过程:Received 24 March 2010, Revised 2 September 2010, Available online 14 December 2010.

论文官网地址:https://doi.org/10.1016/j.cam.2010.11.031