Схема повышенного порядка точности для двумерного уравнения Пуассона в прямоугольнике с учетом влияния краевого условия Дирихле / Майко Н. В. (2018)
Ukrainian

English  Cybernetics and Systems Analysis   /     Issue (2018, 54 (4))

Mayko N.V.
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

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. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: boundary effect, difference operator, Dirichlet boundary condition, error estimate, finite-difference scheme, nine-point template, Poisson’s equation, Finite difference method, Geometry, Poisson equation, Boundary effects, Difference operators, Dirichlet boundary condition, Error estimates, Finite difference scheme, nine-point template, Boundary conditions


Cite:
Mayko N.V. (2018). 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. Cybernetics and Systems Analysis, 54 (4), 122-134. doi: https://doi.org/10.1007/s10559-018-0063-7 http://jnas.nbuv.gov.ua/article/UJRN-0000889051 [In Russian].


 

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