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