Convergence analysis of waveform relaxation methods for neutral differential-functional systems

Authors:
Shulin Wu;Chengming Huang
Affiliations:
Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, PR China;Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

In this paper, the problems of convergence and superlinear convergence of continuous-time waveform relaxation method applied to Volterra type systems of neutral functional-differential equations are discussed. Under a Lipschitz condition with time- and delay-dependent right-hand side imposed on the so-called splitting function, more suitable conditions about convergence and superlinear convergence of continuous-time WR method are obtained. We also investigate the initial interval acceleration strategy for the practical implementation of the continuous-time waveform relaxation method, i.e., discrete-time waveform relaxation method. It is shown by numerical results that this strategy is efficacious and has the essential acceleration effect for the whole computation process.