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Zeitschrift für Analysis und ihre Anwendungen


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Volume 27, Issue 2, 2008, pp. 213–231
DOI: 10.4171/ZAA/1352

Published online: 2008-06-30

Implicit Difference Methods for Quasilinear Differential Functional Equations on the Haar Pyramid

A. Kepczyńska[1]

(1) Gdansk University of Technology, Poland

We present a new class of numerical methods for quasilinear first order partial functional differential equations. The numerical methods are difference schemes which are implicit with respect to the time variable. The existence of approximate solutions is proved by using a theorem on difference inequalities. The proof of the stability is based on a comparison technique with nonlinear estimates of the Perron type for given operators. Numerical experiments are presented. Results obtained in this paper can be applied to differential integral problems and to equations with deviated variables.

Keywords: Initial problems on the Haar pyramid, implicit difference methods, stability and convergence, interpolating operators

Kepczyńska A.: Implicit Difference Methods for Quasilinear Differential Functional Equations on the Haar Pyramid. Z. Anal. Anwend. 27 (2008), 213-231. doi: 10.4171/ZAA/1352