We study a regularized interacting particle method for computing aggregation patterns and
near singular solutions of a Keller–Segel (KS) chemotaxis system in two and three space …

In this paper, we develop a sparse grid stochastic collocation method to improve the
computational efficiency in handling the steady Stokes-Darcy model with random hydraulic …

In this paper, we study the propagation speeds of reaction-diffusion-advection fronts in time-
periodic cellular and chaotic flows with Kolmogorov--Petrovsky--Piskunov (KPP) …

In this paper, we study the convergence analysis for a robust stochastic structure-preserving
Lagrangian numerical scheme in computing effective diffusivity of time-dependent chaotic …

We investigate stochastic modified equations to explain the mathematical mechanism of
symplectic methods applied to rough Hamiltonian systems. The contribution of this paper is …

In this paper, we develop efficient stochastic structure-preserving schemes to compute the
effective diffusivity for particles moving in random flows. We first introduce the motion of a …

We aim to efficiently compute spreading speeds of reaction-diffusion-advection (RDA) fronts
in divergence free random flows under the Kolmogorov-Petrovsky-Piskunov (KPP) …

The quantitative characterization of the evolution of the error distribution (as the step-size
tends to zero) is a fundamental problem in the analysis of stochastic numerical method. In …

In this paper, we study the problem of computing the effective diffusivity for a particle moving
in chaotic flows. Instead of solving a convection-diffusion type cell problem in the Eulerian …

We develop a new framework for error analysis on stochastic numerical schemes, with the
rough path theory and stochastic backward error analysis. Based on our approach, we prove …