Solving Dirichlet's problem in a rectangle for separate variable coefficient elliptic equations
type: Item
instance of: scholarly article
title: Solving Dirichlet's problem in a rectangle for separate variable coefficient elliptic equations
zbMATH Open document ID: 1012.35023
DOI: 10.1016/S0893-9659(02)00029-0
author: R. Smith
published in: Applied Mathematics Letters
publication date: 2002-09-03T00:00:00Z
review text: The authors consider the problem \[ \begin{cases} U_{xx}(x,y) +{A(x) \over B(y)}U_{yy} (x,y)=0, & (x,y)\in(0,1) \times(0,1),\\ U(x,0)=0, & 0\leq x\leq 1\\ U(0,y)=0,\\ U(x,1)= g(x),\\ U(1,y)=0, \end{cases} \tag{1} \] where \(A(x)\geq 0\), \(B(y)\geq 0\), and \(g(x)\) is a given function. They deal with the construction of exact series solutions of (1) using the separation of variables method.
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35A25
zbMATH DE Number: 1794933
zbMATH Keywords: exact series solutions
zbMATH Keywords: separation of variables
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1794933