Convergence of stationary radial basis function-schemes for evolution equations
Numerical Analysis
2019-05-06 v1
Abstract
We establish precise convergence rates for semi-discrete schemes based on Radial Basis Function interpolation, as well as approximate approximation results for such schemes. Our schemes use stationary interpolation on regular grids, with basis functions from a general class of functions generalizing one introduced earlier by M. Buhmann. Our results apply to parabolic equations such as the heat equation or Kolmogorov-Fokker-Planck equations associated to L\'evy processes, but also to certain hyperbolic equations.
Cite
@article{arxiv.1905.01128,
title = {Convergence of stationary radial basis function-schemes for evolution equations},
author = {Brad Baxter and Raymond Brummelhuis},
journal= {arXiv preprint arXiv:1905.01128},
year = {2019}
}