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Cybernetics And Systems Analysis
International Theoretical Science Journal
UDC 519.6
N.V. Mayko1

THE FINITE-DIFFERENCE SCHEME OF HIGHER ORDER OF ACCURACY
FOR THE TWO-DIMENSIONAL POISSON EQUATION IN A RECTANGLE
WITH ALLOWANCE FOR THE EFFECT OF THE DIRICHLET BOUNDARY CONDITION

Abstract. We investigate the finite-difference scheme of higher order of accuracy on a nine-point template for Poisson’s equation in a rectangle with the Dirichlet boundary condition. We substantiate the error estimate taking into account the influence of the boundary condition. We prove that the accuracy order is higher near the sides of the rectangle than at the inner nodes of the mesh set and increase in the approximation order has no impact on the boundary effect.

Keywords: Poisson’s equation, Dirichlet boundary condition, finite-difference scheme, nine-point template, discrete operator, error estimate, boundary effect.



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

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