Numerical method of lines for first order partial differential-functional equations
type: Item
instance of: scholarly article
title: Numerical method of lines for first order partial differential-functional equations
zbMATH Open document ID: 1030.65098
DOI: 10.4171/ZAA/1119
author: A. Baranowska
author: Z. Kamont
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2004-02-08T00:00:00Z
review text: The authors discuss a method to solve the Cauchy problem for a nonlinear equation on the Haar pyramid, by using a discretization with respect to the spatial variables. The partial functional-differential equation is transformed into a system of ordinary functional-differential equations. The authors use differential-inequalities techniques to prove the convergence of the method of lines. Differential equations with retarded variables and differential-integral equations are particular cases of the general model considered in this paper. A numerical example is given to illustrate the theory.
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 34K28
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 35R10
Mathematics Subject Classification ID: 65M12
zbMATH DE Number: 1925961
zbMATH Keywords: Cauchy problem
zbMATH Keywords: differential-difference inequalities
zbMATH Keywords: comparision technique
zbMATH Keywords: stability
zbMATH Keywords: convergence
zbMATH Keywords: Haar pyramid
zbMATH Keywords: partial functional-differential equation
zbMATH Keywords: system of ordinary functional-differential equations
zbMATH Keywords: differential-integral equations
zbMATH Keywords: numerical examples
reviewed by: Seenith Sivasundaram
MaRDI profile type: Publication
cites work: Q3974584
cites work: On the local Cauchy problem for Hamilton Jacobi equations with a functional dependence
cites work: Uniqueness result for the generalized entropy solutions to the Cauchy problem for first-order partial differential-functional equations
cites work: Q3784545
cites work: Q3985397
cites work: Sur le problème de Cauchy pour les systèmes d'équations aux dérivées partielles du premier ordre dans les cas hyperbolique de deux variables indépendantes
cites work: Existence of solutions of a nonlinear boundary value problem via the method of lines
cites work: Q4266267
cites work: Ein Existenzbeweis für nichtlineare parabolische Differentialgleichungen aufgrund der Linientheorie
cites work: Existence and convergence theorems for the boundary layer equations based on the line method
cites work: Existence, Uniqueness, and Numerical Analysis of Solutions of a Quasilinear Parabolic Problem
cites work: Adaptive method of lines
cites work: Convergence of the lines method for first‐order partial differential‐functional equations
cites work: Q4231648
description: scientific article; zbMATH DE number 1925961