Segmented Tau approximation for a parametric nonlinear neutral differential equation

摘要

The segmented formulation of the Tau method is used to approximate the solutions of the parametric nonlinear neutral differential equationy′(t)=ry(t)(a+by(t-τ)+cy′(t-τ)),t⩾0,y(t)=Ψ(t),t⩽0,which represents, for different values of the parameters r, a, b, c and τ, a family of functional differential equations with some of its members arising in areas as different as the number theory, mathematical biology, and population dynamics. For this equation no closed form of analytical solution is available. The numerical results obtained are consistent with the theoretical and practical results reported elsewhere.