Oversampling is a necessity for RBF-collocation method of lines
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We study a radial basis functions least-squares (RBF-LS), a.k.a. kernel-based LS, collocation method of lines [arXiv:2109.03409] for solving surface diffusion problems. Our convergence analysis requires that collocation points has to be sufficiently dense with respect to the RBF centers. In this paper, we further study how oversampling ratio, which is the numbers of collocation points over that of RBF centers for quasi-uniform sets, affects eigenvalue stability, time stepping sizes taken by Runge-Kutta methods, and accuracy.
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