Implicit difference methods for quasilinear differential functional equations on the Haar pyramid
type: Item
instance of: scholarly article
title: Implicit difference methods for quasilinear differential functional equations on the Haar pyramid
zbMATH Open document ID: 1145.65056
DOI: 10.4171/ZAA/1352
author: A. Kępczyńska
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2008-07-02T00:00:00Z
full work available at URL: http://www.ems-ph.org/journals/show_pdf.php
review text: The author presents a new approach to the numerical solution of quasilinear first order partial differential equations. He proves that under natural assumptions on the given functions and on the mesh, there is a class of implicit difference schemes which are convergent. The proof of the stability is based on a comparison technique with nonlinear estimates of the Perron type for the given operators. A numerical experiment is illustrated by an example. Results obtained in this paper can be applied to differential-integral problems.
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 35R10
zbMATH DE Number: 5296726
zbMATH Keywords: initial value problem
zbMATH Keywords: Haar pyramid
zbMATH Keywords: implicit difference methods
zbMATH Keywords: stability
zbMATH Keywords: convergence
zbMATH Keywords: interpolating operators
zbMATH Keywords: quasilinear first order
zbMATH Keywords: numerical experiment
reviewed by: Qin Meng Zhao
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5296726