In this study, a strategy was proposed to determine the interval of the variable shape parameter for the ghost point method using radial basis functions. The determination of a suitable interval for the variable shape parameter remains a challenge. The modified Franke formula was used as an initial predictor of the center of the interval of the variable shape parameter in this study. After extensive tests, a numerical procedure was found for the determination of a suitable interval. The improvement from the imposition of the partial differential equation on the boundary points using the ghost point method was also investigated. To demonstrate the effectiveness of the proposed approach, four numerical examples are presented, including second and fourth order partial differential equations in 2D and 3D.

在这项研究中，提出了一种使用径向基函数确定鬼点法可变形状参数区间的策略。确定可变形状参数的合适区间仍然是一个挑战。在本研究中，修正的 Franke 公式被用作可变形状参数区间中心的初始预测器。经过大量测试，找到了确定合适间隔的数值程序。还研究了使用鬼点方法在边界点上施加偏微分方程的改进。为了证明所提出方法的有效性，给出了四个数值例子，包括 2D 和 3D 中的二阶和四阶偏微分方程。