Numerical Algorithms

, Volume 80, Issue 2, pp 469–483 | Cite as

Convergence of discrete time waveform relaxation methods

  • Zhencheng FanEmail author
Original Paper


This paper concerns the discrete time waveform relaxation (DWR) methods for ordinary differential equations (ODEs). We present a general algorithm of constructing the DWR methods with any order of convergence, which applies any numerical methods of ODEs to the perturbed equations of iterative schemes of continuous time waveform relaxation methods. It is demonstrated that the DWR method presented in this paper has the same convergent order as the numerical method used to discretize perturbed equations. Two classes of interpolation polynomials are given to generate perturbed equations. Finally, numerical experiments are presented in order to check against results obtained.


Convergence Discrete time waveform relaxation methods Interpolation polynomial 

Mathematics Subject Classification (2010)

65L05 65L06 65L20 


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Funding information

This work is supported by the Natural Science Foundation of Fujian Province (2015J01588), the science project municipal university of Fujian Province(JK2014041).


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsMinjiang UniversityFuzhouChina

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