A monotonic finite-difference scheme for a parabolic problem with nonlocal conditions
type: Item
instance of: scholarly article
title: A monotonic finite-difference scheme for a parabolic problem with nonlocal conditions
zbMATH Open document ID: 1030.65092
DOI: 10.1023/A:1021167932414
author: Olga Suboč
author: Raimondas Čiegis
author: A. Štikonas
author: Olga Štikonienẹ
published in: Differential Equations
publication date: 2003-05-25T00:00:00Z
review text: The authors prove convergence, maximum principles, and establish the order of finite difference schemes for solving the following parabolic problem in one space dimension: \[ \varrho(x,t)\frac{\partial u}{\partial t} = \frac{\partial}{\partial x}\left(p(x)\frac{\partial u}{\partial x}\right)- q(x,t) u + f(x,t),\quad (x,t)\in Q_T=(0,1)\times (0,T], \] with initial condition \[ u(x,0)=u^0(x),\quad x\in [0,1], \] and non--local boundary conditions: \[ u(l,t)= \gamma_l \left(\widetilde{\alpha}_l(t) u(\widetilde{x}_l(t),t) + \int_0^1 \widetilde{\beta}_l(x,t) u(x,t) dx \right) + f_l(t), \] for \(t\in (0,T]\), \(l=0,1\). Results for the corresponding stationary problem are also given.
reviewed by: Oscar Lopez-Pouso
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 65M12
zbMATH DE Number: 1916132
zbMATH Keywords: finite difference scheme
zbMATH Keywords: parabolic equation
zbMATH Keywords: nonlocal boundary conditions
zbMATH Keywords: convergence
zbMATH Keywords: maximum principles
MaRDI profile type: Publication
full work available at URL: a:1021167932414
OpenAlex ID: W20755397
description: scientific article; zbMATH DE number 1916132