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This article is cited in 3 scientific papers (total in 3 papers)
Approximate grid solution of a nonlocal boundary value problem for Laplace’s equation on a rectangle
E. A. Volkov Steklov Mathematical Institute of the Russian Academy of Sciences
Abstract:
A nonlocal boundary value problem for Laplace’s 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 Poisson’s equation.
Key words:
nonlocal boundary value problem in a rectangular domain, finite difference method, convergence of discrete solutions.
DOI:
https://doi.org/10.7868/S0044466913080140
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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 Laplace’s equation on a rectangle”, Zh. Vychisl. Mat. Mat. Fiz., 53:8 (2013), 1302–1313; Comput. Math. Math. Phys., 53:8 (2013), 1128–1138
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Citing articles on Google Scholar:
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This publication is cited in the following articles:
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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
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Volkov E.A. Dosiyev A.A., “On the Numerical Solution of a Multilevel Nonlocal Problem”, Mediterr. J. Math., 13:5 (2016), 3589–3604
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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
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