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

Exploring Oversampling in RBF Least-Squares Collocation Method of Lines for Surface Diffusion