4 papers
Superconvergence of the Strang splitting when using the Crank-Nicolson scheme for parabolic PDEs with Dirichlet and oblique boundary conditions
Guillaume Bertoli, Christophe Besse, Gilles Vilmart
We show that the Strang splitting method applied to a diffusion-reaction equation with inhomogeneous general oblique boundary conditions is of order two when the diffusion equation…
Strang splitting method for semilinear parabolic problems with inhomogeneous boundary conditions: a correction based on the flow of the nonlinearity
Guillaume Bertoli, Gilles Vilmart
The Strang splitting method, formally of order two, can suffer from order reduction when applied to semilinear parabolic problems with inhomogeneous boundary conditions. The recent…
Multirevolution integrators for differential equations with fast stochastic oscillations
Adrien Laurent, Gilles Vilmart
We introduce a new methodology based on the multirevolution idea for constructing integrators for stochastic differential equations in the situation where the fast oscillations the…
Explicit Stabilised Gradient Descent for Faster Strongly Convex Optimisation
Armin Eftekhari, Bart Vandereycken, Gilles Vilmart +1
This paper introduces the Runge-Kutta Chebyshev descent method (RKCD) for strongly convex optimisation problems. This new algorithm is based on explicit stabilised integrators for…