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 [Chen et al. SIAM J. Numer. Anal. 61(3), 1386–1404 (2023)]. 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.
Scopus Subject Areas
- Applied Mathematics
- Eigenvalue stability
- Kernel-based least-squares collocation methods
- Method of lines
- Partial differential equations on manifolds
- Surface diffusion