On the validity and stability of the method of lines for the solution of partial differential equations
type: Item
instance of: scholarly article
title: On the validity and stability of the method of lines for the solution of partial differential equations
zbMATH Open document ID: 0619.65105
DOI: 10.1016/0096-3003(87)90038-5
author: Mikhail Naguib Mikhail
published in: Applied Mathematics and Computation
publication date: 1987-01-01T00:00:00Z
review text: The method of lines based on the simplest finite difference replacement of \(\partial^ 2/\partial y^ 2\) is applied to the soluton of the Dirichlet problem for Laplace's equation \(\partial^ 2u/\partial x^ 2+\partial^ 2u/\partial y=0\) in a square in the (x,y)-plane. The standard Fourier series representation of the true and the numerical solutions are given and several perfunctory conclusions are drawn.
Mathematics Subject Classification ID: 65N40
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 4005528
zbMATH Keywords: stability
zbMATH Keywords: Laplace equation
zbMATH Keywords: method of lines
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: Fourier series representation
reviewed by: Jesús María Sanz-Serna
MaRDI profile type: Publication
full work available at URL: 0096-3003(87)90038-5
OpenAlex ID: W2048848076
cites work: A super-element approach for the solution of problems of the boundary value type
cites work: On the numerical solution of elliptic partial differential equations by the method of lines
cites work: The method of straight lines for one-dimensional mixed non-stationary problems and estimation of the mean square error
cites work: A classification and survey of numerical methods for boundary value problems in ordinary differential equations
description: scientific article; zbMATH DE number 4005528