Open Access
november 2013 Method of lines for nonlinear first order partial functional differential equations
A. Szafrańska
Bull. Belg. Math. Soc. Simon Stevin 20(5): 859-880 (november 2013). DOI: 10.36045/bbms/1385390769


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.


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A. Szafrańska. "Method of lines for nonlinear first order partial functional differential equations." Bull. Belg. Math. Soc. Simon Stevin 20 (5) 859 - 880, november 2013.


Published: november 2013
First available in Project Euclid: 25 November 2013

zbMATH: 1282.35397
MathSciNet: MR3160594
Digital Object Identifier: 10.36045/bbms/1385390769

Primary: 35R10 , 65M20

Keywords: Functional differential equations , initial value problems , method of lines , stability and convergence

Rights: Copyright © 2013 The Belgian Mathematical Society

Vol.20 • No. 5 • november 2013
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