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

DOI10.1007/s10092-012-0071-3zbMath1277.35124OpenAlexW2050920414MaRDI QIDQ385441

Krzysztof A. Topolski

Publication date: 2 December 2013

Published in: Calcolo (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10092-012-0071-3

zbMATH Keywords

Cauchy problemfinite difference schemesviscosity solutionsdifferential-functional equations

Mathematics Subject Classification ID

Partial functional-differential equations (35R10) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Viscosity solutions to PDEs (35D40)

Cites Work

• On the existence of viscosity solutions for the parabolic differential-functional Cauchy problem
• Implicit difference schemes for evolution functional differential equations
• Approximation schemes for viscosity solutions of Hamilton-Jacobi equations
• Numerical method of bicharacteristics for hyperbolic partial functional differential equations
• Theory of functional differential equations. 2nd ed
• Introduction to functional differential equations
• Two Approximations of Solutions of Hamilton-Jacobi Equations
• Generalized implicit Euler method for hyperbolic functional differential equations
• Viscosity Solutions of Hamilton-Jacobi Equations
• User’s guide to viscosity solutions of second order partial differential equations
• Convergence results for unbounded solutions of first order non-linear differential-functional equations
• GENERALIZED SOLUTIONS OF NONLINEAR FIRST ORDER EQUATIONS WITH SEVERAL INDEPENDENT VARIABLES. II
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