Abstract
We prove the convergence of meshfree collocation methods for the terminal value problems of fully nonlinear parabolic partial differential equations in the framework of viscosity solutions, provided that the basis function approximations of the terminal condition and the nonlinearities are successful at each time step. A numerical experiment with a radial basis function demonstrates the convergence property.
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Acknowledgements
The author is thankful to the anonymous referees for their useful comments for previous versions of this paper. This study is partially supported by JSPS KAKENHI Grant Number 26800079.
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Nakano, Y. Convergence of meshfree collocation methods for fully nonlinear parabolic equations. Numer. Math. 136, 703–723 (2017). https://doi.org/10.1007/s00211-016-0852-8
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DOI: https://doi.org/10.1007/s00211-016-0852-8