Laguerre series solution of a functional differential equation

This paper presents a Laguerre series method for the solution of a functional differential equation of the type (d/dt)y(t) = Ay(λt) + By(t), with given initial conditions. The method consists of the following steps : (1) represent y(t) and y(λt), respectively, by series of the Laguerre polynomials gi(t) and gi(λt) ; (2) expand gi(λt) into Laguerre series of gi(t) ; (3) integrate the Laguerre series approximation of the functional differential equation by an operational matrix approach. Two numerical examples are given with satisfactory results.