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Cybernetics And Systems Analysis
International Theoretical Science Journal
UDC 519.6
N.V. Mayko

THE WEIGHTED ERROR ESTIMATE OF THE FINITE-DIFFERENCE SCHEME OF THE INCREASED
APPROXIMATION ORDER FOR THE TWO-DIMENSIONAL POISSON EQUATION WITH ALLOWANCE
FOR THE DIRICHLET BOUNDARY CONDITION

Abstract. We obtain the weighted error estimate of the finite-difference scheme of the increased approximation order on a nine-point template for the first boundary-value problem for Poisson’s equation in a rectangle on generalized solutions. The estimate takes into account the influence of the Dirichlet boundary condition and shows that the accuracy order is higher near the sides of the rectangle than at the inner points of the mesh set.

Keywords: Poisson’s equation, boundary value problem, Dirichlet’s boundary condition, finite-difference scheme, weighted error estimate, boundary effect.



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Taras Shevchenko National University of Kyiv, Kyiv, Ukraine,
e-mail: mayko@knu.ua.

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