Premium
A Cauchy integral method of the solution of the 2D Dirichlet problem for simply or doubly connected domains
Author(s) -
Shirokova Elena A.,
ElShenawy Atallah
Publication year - 2018
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22290
Subject(s) - mathematics , mathematical analysis , dirichlet problem , integral equation , dirichlet integral , laplace's equation , cauchy distribution , boundary value problem , dirichlet boundary condition , dirichlet distribution , laplace transform , fredholm integral equation , fourier series , cauchy's integral formula , cauchy problem , dirichlet's energy , initial value problem
In this paper we propose a new method for solving the 2D Laplace equation with Dirichlet boundary conditions in simply and doubly connected domains. Here, we apply the numerical algorithm based on truncated Fourier series and reduce the corresponding Fredholm integral equation to a finite system of linear equations.