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Zeitschrift für Analysis und ihre Anwendungen

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Volume 21, Issue 4, 2002, pp. 949–962
DOI: 10.4171/ZAA/1119

Published online: 2002-12-31

Numerical Method of Lines for First Order Partial Differential-Functional Equations

Anna Baranowska[1] and Zdzisław Kamont[2]

(1) Polish Naval Academy, Gdynia, Poland
(2) University of Gdansk, Poland

We consider the Cauchy problem for a nonlinear equation on the Haar pyramid. By using a discretization with respect to spatial variables, the partial functional-differential equation is transformed into a system of ordinary functional-differential equations. We investigate the question of under what conditions the classical solutions of the original problem are approximated by solutions of associated systems of ordinary functional-differential equations. The proof of the convergence of the method of lines is based on the differentialinequalities technique. A numerical example is given. Differential equations with retarded variables and differential-integral equations are particular cases of a general model considered in the paper.

Keywords: Cauchy problem, differential-difference inequalities, comparison technique, stability and convergence

Baranowska Anna, Kamont Zdzisław: Numerical Method of Lines for First Order Partial Differential-Functional Equations. Z. Anal. Anwend. 21 (2002), 949-962. doi: 10.4171/ZAA/1119