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Zh. Vychisl. Mat. Mat. Fiz., 2013, Volume 53, Number 8, Pages 1302–1313 (Mi zvmmf9902)  

This article is cited in 3 scientific papers (total in 3 papers)

Approximate grid solution of a nonlocal boundary value problem for Laplaces equation on a rectangle

E. A. Volkov

Steklov Mathematical Institute of the Russian Academy of Sciences

Abstract: A nonlocal boundary value problem for Laplaces equation on a rectangle is considered. Dirichlet boundary conditions are set on three sides of the rectangle, while the boundary values on the fourth side are sought using the condition that they are equal to the trace of the solution on the parallel midline of the rectangle. A simple proof of the existence and uniqueness of a solution to this problem is given. Assuming that the boundary values given on three sides have a second derivative satisfying a Hölder condition, a finite difference method is proposed that produces a uniform approximation (on a square mesh) of the solution to the problem with second order accuracy in space. The method can be used to find an approximate solution of a similar nonlocal boundary value problem for Poissons equation.

Key words: nonlocal boundary value problem in a rectangular domain, finite difference method, convergence of discrete solutions.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00744
Ministry of Education and Science of the Russian Federation -6431.2012.1
Russian Academy of Sciences - Federal Agency for Scientific Organizations


DOI: https://doi.org/10.7868/S0044466913080140

Full text: PDF file (222 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2013, 53:8, 1128–1138

Bibliographic databases:

UDC: 519.632.4
Received: 14.03.2013

Citation: E. A. Volkov, “Approximate grid solution of a nonlocal boundary value problem for Laplaces equation on a rectangle”, Zh. Vychisl. Mat. Mat. Fiz., 53:8 (2013), 1302–1313; Comput. Math. Math. Phys., 53:8 (2013), 1128–1138

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. A. Volkov, “Solvability analysis of a nonlocal boundary value problem by applying the contraction mapping principle”, Comput. Math. Math. Phys., 53:10 (2013), 1494–1498  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. Volkov E.A. Dosiyev A.A., “On the Numerical Solution of a Multilevel Nonlocal Problem”, Mediterr. J. Math., 13:5 (2016), 3589–3604  crossref  mathscinet  zmath  isi  scopus
    3. Dosiyev A.A., “Difference Method of Fourth Order Accuracy For the Laplace Equation With Multilevel Nonlocal Conditions”, J. Comput. Appl. Math., 354 (2019), 587–596  crossref  mathscinet  isi  scopus
  •      Computational Mathematics and Mathematical Physics
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