Convergence of Linear Multistep Methods for a Class of Delay-Integro-Differential Equations

Abstract

We give a class of step-by-step methods for the numerical solution of delay-integro-differential equations of the form $y'\left( t \right) = G\left( {t,y\left( t \right),\int_{t - \tau }^t {K\left( {t,s,y\left( s \right)} \right)ds} } \right)\quad \left( {t \geqslant 0} \right)$ where τ is fixed, subject to an appropriate initial condition. We present a theory giving the order of convergence of such methods.