A new computer-assisted analytic method for the Dirichlet and Neumann problems
type: Item
instance of: scholarly article
title: A new computer-assisted analytic method for the Dirichlet and Neumann problems
zbMATH Open document ID: 0629.65121
DOI: 10.4171/ZAA/232
author: Herbert H. Snyder
author: Ralph W. Wilkerson
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1987-01-01T00:00:00Z
review text: The authors introduce a new method for the Dirichlet and Neumann problems (in \({\mathbb{R}}^ 2\) and \({\mathbb{R}}^ 3)\) based on certain theorems of S. Zaremba and S. Bergmann. With the help of a symbolic computing language (FORMAC with PL/1), the authors show how it is possible to orthonormalize a complete sequence of harmonic polynomials on the domain G of the solution. The solution is then given by an expansion in these orthonormalized polynomials. Under certain conditions on the boundary values, the expansion coefficients themselves may also be automatically calculated.
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 4024712
zbMATH Keywords: Dirichlet's problem
zbMATH Keywords: expansion in orthonormal polynomials
zbMATH Keywords: Laplace equation
zbMATH Keywords: Neumann problems
zbMATH Keywords: symbolic computing language
zbMATH Keywords: FORMAC with PL/1
zbMATH Keywords: harmonic polynomials
zbMATH Keywords: expansion coefficients
describes a project that uses: PL/I
describes a project that uses: FORMAC
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/zaa/232
OpenAlex ID: W2564957983
Recommended article: A numerical method for the nonlinear Neumann problem
Recommended article: A computational approach for the analytical solving of a Dirichlet-type problem for third order partial differential equations
Recommended article: On finite element methods for the Neumann problem
Recommended article: Q4933906
Recommended article: A spectral method for elliptic equations: The Neumann problem
Recommended article: Q3645660
Recommended article: A computational approach for the analytical solving of partial differential equations
Recommended article: Computer-assisted enclosure methods for elliptic differential equations
Recommended article: Dirichlet-Neumann and Neumann-Neumann waveform relaxation algorithms for parabolic problems
Recommended article: Q3343371
description: scientific article; zbMATH DE number 4024712