The Finite-Difference Scheme of Higher Order of Accuracy for the Two-Dimensional Poisson Equation in a Rectangle with Regard for the Effect of the Dirichlet Boundary Condition

s 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 o...

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Veröffentlicht in:Cybernetics and systems analysis 2018-07, Vol.54 (4), p.624-635
1. Verfasser: Mayko, N. V.
Format: Artikel
Sprache:eng
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Zusammenfassung:s 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 grid set and increase in the approximation order has no impact on the boundary effect.
ISSN:1060-0396
1573-8337
DOI:10.1007/s10559-018-0063-7