On error estimates for waveform relaxation methods for delay-differential equations

摘要

In this paper the problem of delay-dependent error estimates for waveform relaxation methods applied to systems of delay-differential equations is discussed. Under suitable conditions imposed on the so-called splitting function it is shown how the error estimates depend on the character of delays and how much these estimates are better than the known error estimates for relaxation methods. We attempt to derive the error estimates as sharp as possible under the assumed conditions. Our approach takes into account the specific properties of the considered equations. It is also proved that under some assumptions the exact solution can be obtained after a finite number of steps of the iterative process; i.e., we prove that the waveform relaxation methods have the same property as the classical method of steps for solving delay-differential equations with nonvanishing delays. From the given estimates the number of these steps can be found. [References: 13]