Convergence of stationary radial basis function-schemes for evolution equations
Provides theoretical convergence guarantees for RBF-based numerical schemes, benefiting researchers in numerical analysis and scientific computing.
The paper establishes precise convergence rates for semi-discrete schemes using stationary Radial Basis Function interpolation on regular grids, applying to parabolic and hyperbolic equations.
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 Lévy processes, but also to certain hyperbolic equations.