Numerical methods for hyperbolic functional differential problems on the Haar pyramid
type: Item
instance of: scholarly article
title: Numerical methods for hyperbolic functional differential problems on the Haar pyramid
zbMATH Open document ID: 0964.65094
author: D. Jaruzewska-Walzak
author: Z. Kamont
published in: Computing
publication date: 2001-06-26T00:00:00Z
review text: The main topic of the paper is the numerical solution of the Cauchy problem for a system of nonlinear hyperbolic functional differential equations. The authors propose a wide introduction to orient the reader within the literature on this topic. Next they construct a general class of difference methods and prove a theorem on their convergence. Then in the two subsequent sections the authors define interpolating operators on the Haar pyramid, use nonlinear estimates of the Perron type for given functions with respect to the functional variable to obtain results on the error estimate for approximate solutions and apply functional difference inequalities for the stability result. Numerical examples are reported ad the end of the paper.
reviewed by: Riccardo Fazio
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 35L60
Mathematics Subject Classification ID: 35R10
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M15
zbMATH DE Number: 1523190
zbMATH Keywords: initial value problems
zbMATH Keywords: interpolating operators
zbMATH Keywords: functional difference inequalities
zbMATH Keywords: nonlinear estimates of the Perron type
zbMATH Keywords: error estimates
zbMATH Keywords: system of nonlinear hyperbolic functional differential equations
zbMATH Keywords: Cauchy problem
zbMATH Keywords: difference methods
zbMATH Keywords: convergence
zbMATH Keywords: Haar pyramid
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1523190