Stability properties of a scheme for the approximate solution of a delay- integro-differential equation
The authors study stability properties of a numerical scheme applied to Volterra integro-differential equations with finite memory of the form \(y'(t)=G(t,y(t),\int^ t_{t-\tau}K(t,s,y(s))ds\), \(t\geq 0\), \(y(t)=\psi(t)\), \((-\tau\leq t<0)\), where \(G\), \(K\) and \(\psi\) are given smooth functions. This numerical scheme is based on a strongly-stable linear multistep formula and a consistent quadrature rule.
Volterra integro-differential equations with finite memory
strongly-stable linear multistep formula
scientific article; zbMATH DE number 54686
scientific article