Remarks on waveform relaxation method with overlapping splittings. (English) Zbl 0907.65063

This paper is concerned with the strategy of overlapping splittings in using waveform relaxation methods on finite time intervals. Starting from the iteration operator and its resolvent, the order of the iteration operator turns out to be the decisive quantity for the valuation of the method. It is shown that this order may decrease if overlapping is used, and further, how overlapping should be done to best accelerate of the iterative method. The results are illustrated in treating band matrices.


65L05 Numerical methods for initial value problems involving ordinary differential equations
65F10 Iterative numerical methods for linear systems
34A30 Linear ordinary differential equations and systems
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