Spectral Approximation of Time Windows in the Solution of Dissipative Linear Differential Equations

Keywords: Linear differential systems, time window, spectral approximation, waveform
relaxation.

Abstract: We establish a relation between the length T of the integration window of a linear
differential equation x’+Ax = b and a spectral parameter s*. This parameter is determined
by comparing the exact solution x(T) at the end of the integration window to the solution
of a linear system obtained from the Laplace transform of the differential equation by
freezing the system matrix. We propose a method to integrate the relation s* = s*(T) into
the determination of the interval of rapid convergence of waveform relaxation iterations.
The method is illustrated with a few numerical examples.

 

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