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首页> 外文会议>International Conference "Functional Analysis in Interdisciplinary Applications" >A Highly Accurate Difference Method for Solving the Dirichlet Problem for Laplace's Equation on a Rectangle
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A Highly Accurate Difference Method for Solving the Dirichlet Problem for Laplace's Equation on a Rectangle

机译：一种高度准确的差异方法，用于求解拉普勒拉普拉斯等式的Dirichlet问题

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O(h8) order (h is the mesh size) of accurate three-stage difference method on a square grid for the approximate solution of the Dirichlet problem for Laplace's equation on a rectangle is proposed and justified without taking more than 9 nodes of the grid. At the first stage, by using the 9-point scheme the sum of the pure fourth derivatives of the desired solution is approximated of order O(h~6). At the second stage, approximate values of the sum of the pure eighth derivatives is approximated of order O(h~2) by the 5-point scheme. At the final third stage, the system of simplest 5-point difference equations approximating the Dirichlet problem is corrected by introducing the quantities determined at the first and second stages. Numerical experiment is illustrated to support the analysis made.
机译：o（h8）订单（h是网格尺寸）在方形网格上的精确三阶段差异方法的准确三级差异方法，用于Laplace的等式的Dirichlet问题的近似解，并且是合理的，而不是超过9个网格的节点。在第一阶段，通过使用9点方案，所需溶液的纯第四衍生物的和近似的顺序O（H〜6）。在第二阶段，纯第八衍生物的总和的近似值由5点方案近似为Order O（H〜2）。在最终的第三阶段，通过在第一和第二阶段中引入确定的数量来校正近似Dirichlet问题的最简单5点差分方程的系统。说明了数值实验以支持分析。

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