, Volume 50, Issue 4, pp 329-343

First online:

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

  • Krzysztof A. TopolskiAffiliated withInstitute of Mathematics, University of Gdaǹsk Email author 


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.


Viscosity solutions Cauchy problem Differential-functional equations Finite difference schemes

Mathematics Subject Classification (2010)

35D40 35R10 65M15 65M06