December 2013, Volume 50, Issue 4, pp 329343,
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 differentialfunctional Cauchy problem
 Krzysztof A. Topolski
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Abstract
We consider the Cauchy problem for first order differentialfunctional 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 differentialintegral equation. Numerical examples to illustrate the theory are presented.
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 Title
 On the numerical approximation of viscosity solutions for the differentialfunctional Cauchy problem
 Open Access
 Available under Open Access This content is freely available online to anyone, anywhere at any time.
 Journal

Calcolo
Volume 50, Issue 4 , pp 329343
 Cover Date
 20131201
 DOI
 10.1007/s1009201200713
 Print ISSN
 00080624
 Online ISSN
 11265434
 Publisher
 Springer Milan
 Additional Links
 Topics
 Keywords

 Viscosity solutions
 Cauchy problem
 Differentialfunctional equations
 Finite difference schemes
 35D40
 35R10
 65M15
 65M06
 Authors

 Krzysztof A. Topolski ^{(1)}
 Author Affiliations

 1. Institute of Mathematics, University of Gdaǹsk, Wit Stwosz 57, 80952, Gdaǹsk, Poland