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TW 340
T. Luzyanina, K. Engelborghs, D. Roose
Computing stability of differential equations with bounded distributed delay
Abstract
This paper concerns stability analysis of scalar delay integro-differential equations (DIDEs). We propose a numerical scheme which involves a linear multistep method as time integration scheme and a quadrature method based on Lagrange interpolation and a Gauss-Legendre quadrature rule. We investigate properties of the proposed scheme with respect to preserving stability properties of the original equation. We derive and prove a sufficient condition for stability of a DIDE (with a constant kernel) which we call RHP-stability. Conditions are obtained under which the proposed quadrature preserves RHP-stability. We compare the obtained results with corresponding ones using Newton-Cotes formulas. Results of numerical experiments on computing stability of DIDEs with constant and non-constant kernel functions are presented.
report.pdf / mailto: T. Luzyanina