In this paper a fourth order finite difference ghost point method for the Poisson equation on regular Cartesian mesh is presented. The method can be considered the high order extension of the second ghost method introduced earlier by the authors. Three different discretizations are considered, which differ in the stencil that discretizes the Laplacian and the source term. It is shown that only two of them provide a stable method. The accuracy of such stable methods are numerically verified on several test problems.

翻译：本文提出了一种在规则笛卡尔网格上求解泊松方程的四阶有限差分幽灵点方法。该方法可视为作者先前提出的二阶幽灵点方法的高阶扩展。文中考虑了三种不同的离散化方案，其区别在于离散拉普拉斯算子及源项时所采用的模板。研究表明，仅其中两种方案能提供稳定的数值方法。通过多个测试算例，对这类稳定方法的精度进行了数值验证。