Experimental investigation of the block method for the Laplace equation on polygons
type: Item
instance of: scholarly article
title: Experimental investigation of the block method for the Laplace equation on polygons
zbMATH Open document ID: 0968.65096
author: A. K. Kornoukhov
author: E. A. Yakovleva
author: E. A. Volkov
published in: Computational Mathematics and Mathematical Physics
publication date: 2001-09-02T00:00:00Z
review text: The real characteristics of the block method are investigated as applied to the numerical solution of two special boundary value problems. The Dirichlet problem is solved on a square with a cut when the perturbation is concentrated at the end of the cut, and a modified mixed boundary value problem involving an unknown parameter and subject to an additional nonlocal condition is solved on a trapezium. Experimental investigations exhibit the fast convergence of the approximate solution and prove the stability of the method with respect to roundoff errors.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65N15
zbMATH DE Number: 1472975
zbMATH Keywords: Laplace equation
zbMATH Keywords: boundary value problem
zbMATH Keywords: numerical examples
zbMATH Keywords: block method
zbMATH Keywords: error bounds
zbMATH Keywords: integral equation method
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: convergence
zbMATH Keywords: stability
reviewed by: A. Tret'yakov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1472975