Convergent collocation methods for parabolic equations
Yumiharu Nakano · arXiv (Cornell University) · 2018
We show that the functions constructed by the collocation methods with Wendland kernels converge to unique viscosity solutions of the corresponding fully nonlinear parabolic equations. The key ingredients in our proof are the stability property of Wendland kernels that states the norms of the interpolation operators are bounded provided that the inverses of the interpolation matrices exhibit good decays, and the max-min representations of the nonlinearities of the equations. Several numerical experiments support our assumption and result.