# Convergence of stationary radial basis function-schemes for evolution equations

## TL;DR

This paper proves convergence rates for semi-discrete radial basis function schemes applied to evolution equations, including parabolic and hyperbolic types, using stationary interpolation on regular grids.

## Contribution

It introduces precise convergence analysis for RBF-based schemes on regular grids, extending previous work with a broader class of basis functions.

## Key findings

- Established convergence rates for RBF schemes on evolution equations.
- Extended applicability to parabolic and hyperbolic equations.
- Provided approximate approximation results for these schemes.

## 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.