Year: 2020
Type: article
Abstract: In this work, we consider the curvilinear integral equation of the external Dirichlet boundary value problem for the Laplace equation.We divide the curve into elementary parts and establish a quadrature formula at some chosen control points for one class of curvilinear integrals.Then we replace the integral equation with the system of algebraic equations.We also establish the existence and uniqueness of the solution of this system, prove the convergence of its solution to the exact solution of the external Dirichlet boundary value problem for the Laplace equation at the control points, and determine the convergence rate of the method.Besides, we construct a sequence which converges to the solution of the external Dirichlet boundary value problem for the Laplace equation and provide an error estimate.
DOI: 10.29228/proc.44
Author: Mehpara N. Bakhshaliyeva
Institution: Azerbaijan State Oil and Industry University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W3118236901