Simulating diffusion processes in discontinuous media: A numerical scheme with constant time steps

A Scheme for Simulating One-dimensional Diffusion Processes with Discontinuous Coefficients

The aim of this article is to provide a scheme for simulating diffusion processes evolving in one-dimensional discontinuous media. This scheme does not rely on smoothing the coefficients that appear in the infinitesimal generator of the diffusion processes, but uses instead an exact description of the behavior of their trajectories when they reach the points of discontinuity. This description i...

Numerical Diffusion Control of a Space-Time Discontinuous Galerkin Method

Variations on space-time Discontinuous Galerkin (STDG) discretization associated to Runge-Kutta schemes are developed. These new schemes while keeping the original scheme order can improve accuracy and stability. Numerical analysis is made on academic test cases and efficiency of these schemes are shown on propagating pressure waves. AMS subject classifications: 52B10, 65D18, 68U05, 68U07

Simulating Turduckened Black Holes with a Discontinuous Galerkin Scheme

A numerical scheme for space-time fractional advection-dispersion equation

In this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. We utilize spectral-collocation method combining with a product integration technique in order to discretize the terms involving spatial fractional order derivatives that leads to a simple evaluation of the related terms. By using Bernstein polynomial basis, the problem is transformed in...

STEPS: Modeling and Simulating Complex Reaction-Diffusion Systems with Python

We describe how the use of the Python language improved the user interface of the program STEPS. STEPS is a simulation platform for modeling and stochastic simulation of coupled reaction-diffusion systems with complex 3-dimensional boundary conditions. Setting up such models is a complicated process that consists of many phases. Initial versions of STEPS relied on a static input format that did...