Bulletin of the Belgian Mathematical Society - Simon Stevin

Method of lines for nonlinear first order partial functional differential equations

A. Szafrańska

Full-text: Open access

Abstract

Classical solutions of initial problems for nonlinear functional differential equations of Hamilton--Jacobi type are approximated by solutions of associated differential difference systems. A method of quasilinearization is adopted. Sufficient conditions for the convergence of the method of lines and error estimates for approximate solutions are given. Nonlinear estimates of the Perron type with respect to functional variables for given operators are assumed. The proof of the stability of differential difference problems is based on a comparison technique. The results obtained here can be applied to differential integral problems and differential equations with deviated variables.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 20, Number 5 (2013), 859-880.

Dates
First available in Project Euclid: 25 November 2013

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1385390769

Digital Object Identifier
doi:10.36045/bbms/1385390769

Mathematical Reviews number (MathSciNet)
MR3160594

Zentralblatt MATH identifier
1282.35397

Subjects
Primary: 35R10: Partial functional-differential equations 65M20: Method of lines

Keywords
functional differential equations initial value problems method of lines stability and convergence

Citation

Szafrańska, A. Method of lines for nonlinear first order partial functional differential equations. Bull. Belg. Math. Soc. Simon Stevin 20 (2013), no. 5, 859--880. doi:10.36045/bbms/1385390769. https://projecteuclid.org/euclid.bbms/1385390769


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