, Volume 50, Issue 4, pp 329-343,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 18 Oct 2012

On the numerical approximation of viscosity solutions for the differential-functional Cauchy problem

Abstract

We consider the Cauchy problem for first order differential-functional equations. We present finite difference schemes to approximate viscosity solutions of this problem. The functional dependence in the equation is of the Hale type. It contains, as a particular case, equation with a retarded and deviated argument, and differential-integral equation. Numerical examples to illustrate the theory are presented.