On the numerical solution of the diffusion equation with a nonlocal boundary condition
type: Item
instance of: scholarly article
title: On the numerical solution of the diffusion equation with a nonlocal boundary condition
zbMATH Open document ID: 1068.65115
DOI: 10.1155/S1024123X03111015
author: Mehdi Dehghan
published in: Mathematical Problems in Engineering
publication date: 2005-05-09T00:00:00Z
full work available at URL: https://eudml.org/doc/51528
review text: Summary: Parabolic partial differential equations with nonlocal boundary specifications feature in the mathematical modeling of many phenomena. In this paper, numerical schemes are developed for obtaining approximate solutions to the initial boundary value problem for one-dimensional diffusion equation with a nonlocal constraint in place of one of the standard boundary conditions. The method of lines semidiscretization approach is used to transform the model partial differential equation into a system of first-order linear ordinary differential equations (ODEs). The partial derivative with respect to the space variable is approximated by a second-order finite-difference approximation. The solution of the resulting system of first-order ODEs satisfies a recurrence relation which involves a matrix exponential function. Numerical techniques are developed by approximating the exponential matrix function in this recurrence relation. We use a partial fraction expansion to compute the matrix exponential function via Padé approximations, which is particularly useful in parallel processing. The algorithm is tested on a model problem from the literature.
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 65L12
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 2166710
zbMATH Keywords: parallel computation
zbMATH Keywords: numerical example
zbMATH Keywords: nonlocal boundary condition
zbMATH Keywords: initial boundary value problem
zbMATH Keywords: diffusion equation
zbMATH Keywords: method of lines
zbMATH Keywords: second-order finite-difference approximation
zbMATH Keywords: matrix exponential function
zbMATH Keywords: Padé approximations
zbMATH Keywords: algorithm
zbMATH Keywords: semidiscretization
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2166710