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

被引：3

作者：

Mayko, N., V ^{[1
]}

机构：

[1] Taras Shevchenko Natl Univ Kyiv, Kiev, Ukraine

来源：

CYBERNETICS AND SYSTEMS ANALYSIS | 2018年 / 54卷 / 04期

关键词：

Poisson's equation; Dirichlet boundary condition; finite-difference scheme; nine-point template; difference operator; error estimate; boundary effect;

D O I：

10.1007/s10559-018-0063-7

中图分类号：

TP3 [计算技术、计算机技术];

学科分类号：

0812 ;

摘要：

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.

引用

页码：624 / 635

页数：12

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