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We introduce a semi-implicit Milstein approximation scheme for some class of non-colliding particle systems modeled by systems of stochastic differential equations with non-constant diffusion coefficients. We show that the scheme converges…
The effective, fast transport of matter through porous media is often characterized by complex dispersion effects. To describe in mathematical terms such situations, instead of a simple macroscopic equation (as in the classical Darcy's…
In this paper, the design and analysis of high order accurate IMEX finite volume schemes for the compressible Euler-Poisson (EP) equations in the quasineutral limit is presented. As the quasineutral limit is singular for the governing…
We propose a new scheme for the long time approximation of a diffusion when the drift vector field is not globally Lipschitz. Under this assumption, regular explicit Euler scheme --with constant or decreasing step-- may explode and implicit…
An implicit Euler finite-volume scheme for general cross-diffusion systems with volume-filling constraints is proposed and analyzed. The diffusion matrix may be nonsymmetric and not positive semidefinite, but the diffusion system is assumed…
We present a parametric family of semi-implicit second order accurate numerical methods for non-conservative and conservative advection equation for which the numerical solutions can be obtained in a fixed number of forward and backward…
The numerical solution of a nonlinear and space-fractional anti-diffusive equation used to model dune morphodynamics is considered. Spatial discretization is effected using a finite element method whereas the Crank-Nicolson scheme is used…
Time fractional advection-dispersion equations arise as generalizations of classical integer order advection-dispersion equations and are increasingly used to model fluid flow problems through porous media. In this paper we develop an…
This article investigates matrix-free higher-order discontinuous Galerkin discretizations of the Navier--Stokes equations for incompressible flows with variable viscosity. The viscosity field may be prescribed analytically or governed by a…
As fractional diffusion equations can describe the early breakthrough and the heavy-tail decay features observed in anomalous transport of contaminants in groundwater and porous soil, they have been commonly employed in the related…
In this work, we show high order splitting methods of integration without negative steps, allowing us to solve numerically irreversible problems, like reaction-diffusion equations. The methods consist in a suitable affine combinations of…
We propose a new class of semi-implicit methods for solving nonlinear fractional differential equations and study their stability. Several versions of our new schemes are proved to be unconditionally stable by choosing suitable parameters.…
Nonlinear elliptic problems arise in many fields, including plasma physics, astrophysics, and optimal transport. In this article, we propose a novel operator-splitting/finite element method for solving such problems. We begin by introducing…
The advection-diffusion and wave equations are the fundamental equations governing any physical law and therefore arise in many areas of physics and astrophysics. For complex problems and geometries, only numerical simulations can give…
We consider a wide class of semi linear Hamiltonian partial differential equa- tions and their approximation by time splitting methods. We assume that the nonlinearity is polynomial, and that the numerical tra jectory remains at least uni-…
We study the rate of convergence of an explicit and an implicit-explicit finite difference scheme for linear stochastic integro-differential equations of parabolic type arising in non-linear filtering of jump-diffusion processes. We show…
In this paper, we investigate a sequentially decoupled numerical method for solving the fully coupled quasi-static thermo-poroelasticity problems with nonlinear convective transport. The symmetric interior penalty discontinuous Galerkin…
Recent applications (e.g. active gels and self-assembly of elastic sheets) motivate the need to efficiently simulate the dynamics of thin elastic sheets. We present semi-implicit time stepping algorithms to improve the time step constraints…
In this article, we consider discrete schemes for a fractional diffusion equation involving a tempered fractional derivative in time. We present a semi-discrete scheme by using the local discontinuous Galerkin (LDG) discretization in the…
Simulating physical problems involving multi-time scale coupling is challenging due to the need of solving these multi-time scale processes simultaneously. In response to this challenge, this paper proposed an explicit multi-time step…