Lyapunov functions are an essential tool in the stability analysis of dynamical systems, both
in theory and applications. They provide sufficient conditions for the stability of equilibria or …

We introduce a priori Sobolev-space error estimates for the solution of arbitrary nonlinear,
and possibly parametric, PDEs that are defined in the strong sense, using Gaussian process …

In this work, we investigate the spatiotemporal dynamics of reaction–diffusion equations
subject to cross-diffusion in the frame of a two-dimensional ratio-dependent predator–prey …

In this work we develop the standard Hermite interpolation based RBF-generated finite
difference (RBF-HFD) method into a new faster and more accurate technique based on …

Lyapunov functions are an important tool to determine the basin of attraction of equilibria in
Dynamical Systems through their sublevel sets. Recently, several numerical construction …

We proposed ways to implement meshless collocation methods extrinsically for solving
elliptic PDEs on smooth, closed, connected, and complete Riemannian manifolds with …

This is “my” part of a future book “Scientific Computing with Radial Basis Functions” I am
currently writig with my colleagues CS Chen and YC Hon. I took a preliminary version out of …

Methods have previously been developed for the approximation of Lyapunov functions
using radial basis functions. However these methods assume that the evolution equations …

We analyze a least-squares strong-form kernel collocation formulation for solving second-
order elliptic PDEs on smooth, connected, and compact surfaces with bounded geometry …

Meshfree, kernel-based spatial discretisations are recent tools to discretise partial
differential equations on surfaces. The goals of this paper are to analyse and compare three …