This paper investigates the numerical behavior of the radial basis functions least-squares collocation (RBF-LSC) method of lines (MoL) for solving surface diffusion problems, building upon the theoretical analysis presented in [SIAM J. Numer. Anal., 61 (3), 1386-1404}]. Specifically, we examine the impact of the oversampling ratio, defined as the number of collocation points used over the number of RBF centers for quasi-uniform sets, on the stability of the eigenvalues, time stepping sizes taken by Runge-Kutta methods, and overall accuracy of the method. By providing numerical evidence and insights, we demonstrate the importance of the oversampling ratio for achieving accurate and efficient solutions with the RBF-LSC-MoL method. Our results reveal that the oversampling ratio plays a critical role in determining the stability of the eigenvalues, and we provide guidelines for selecting an optimal oversampling ratio that balances accuracy and computational efficiency.

翻译：本文基于文献[SIAM J. Numer. Anal., 61 (3), 1386-1404]的理论分析，研究了径向基函数最小二乘配点(RBF-LSC)方法结合线法用于求解表面扩散问题的数值行为。具体而言，我们考察了过采样比（定义为准均匀点集上使用的配点数量与RBF中心数量之比）对特征值稳定性、Runge-Kutta方法时间步长选取以及方法整体精度的影响。通过提供数值证据和深入分析，我们论证了过采样比对于使用RBF-LSC-MoL方法获得精确高效解的重要性。研究结果表明，过采样比在决定特征值稳定性方面起着关键作用，我们据此提出了平衡计算精度与效率的最优过采样比选取准则。