Related papers: A Family of Second Order Time Stepping Methods for…
This article concerns second-order time discretization of subdiffusion equations with time-dependent diffusion coefficients. High-order differentiability and regularity estimates are established for subdiffusion equations with…
We propose in this paper efficient first/second-order time-stepping schemes for the evolutional Navier-Stokes-Nernst-Planck-Poisson equations. The proposed schemes are constructed using an auxiliary variable reformulation and sophisticated…
This paper develops a two-level fourth-order scheme for solving time-fractional convection-diffusion-reaction equation with variable coefficients subjected to suitable initial and boundary conditions. The basis properties of the new…
In this paper, a second order finite difference scheme is investigated for time-dependent one-side space fractional diffusion equations with variable coefficients. The existing schemes for the equation with variable coefficients have…
This report presents a low computational and cognitive complexity, stable, time accurate and adaptive method for the Navier-Stokes equations. The improved method requires a minimally intrusive modification to an existing program based on…
In this paper we propose a numerical method to solve a 2D advection-diffusion equation, in the highly oscillatory regime. We use an efficient and robust integrator which leads to an accurate approximation of the solution without any time…
We investigate a second-order accurate time-stepping scheme for solving a time-fractional diffusion equation with a Caputo derivative of order~$\alpha \in (0,1)$. The basic idea of our scheme is based on local integration followed by linear…
We propose two stable and one conditionally stable finite difference schemes of second-order in both time and space for the time-fractional diffusion-wave equation. In the first scheme, we apply the fractional trapezoidal rule in time and…
This paper is part of a program to combine a staggered time and staggered spatial discretization of continuum wave equations so that important properties of the continuum that are proved using vector calculus can be proven in an analogous…
Efficient and energy stable high order time marching schemes are very important but not easy to construct for the study of nonlinear phase dynamics. In this paper, we propose and study two linearly stabilized second order semi-implicit…
In this paper, we present a novel explicit second order scheme with one step for solving the forward backward stochastic differential equations, with the Crank-Nicolson method as a specific instance within our proposed framework. We first…
We present and analyze in a unified setting two schemes for the numerical discretization of a Darcy-Forchheimer fluid flow model coupled with an advection-diffusion equation modeling the temperature distribution in the fluid. The first…
We propose and study two second-order in time implicit-explicit (IMEX) methods for the coupled Stokes-Darcy system that governs flows in karst aquifers. The first is a combination of a second-order backward differentiation formula and the…
This paper is concerned with moving mesh finite difference solution of partial differential equations. It is known that mesh movement introduces an extra convection term and its numerical treatment has a significant impact on the stability…
This report considers a variable step time discretization algorithm proposed by Dahlquist, Liniger and Nevanlinna and applies the algorithm to the unsteady Stokes/Darcy model. Although long-time forgotten and little explored, the algorithm…
We study a second order BDF (Backward Differentiation Formula) scheme for the numerical approximation of parabolic HJB (Hamilton-Jacobi-Bellman) equations. The scheme under consideration is implicit, non-monotone, and second order accurate…
We present a class of new explicit and stable numerical algorithms to solve the spatially discretized linear heat or diffusion equation. After discretizing the space and the time variables like conventional finite difference methods, we do…
This paper considers a two-step fourth-order modified explicit Euler/Crank-Nicolson numerical method for solving the time-variable fractional mobile-immobile advection-dispersion model subjects to suitable initial and boundary conditions.…
A new time discretization scheme for the numerical simulation of two-phase flow governed by a thermodynamically consistent diffuse interface model is presented. The scheme is consistent in the sense that it allows for a discrete in time…
In this paper, we propose a new second-order fast finite difference scheme in time for solving the Tempered Time Fractional Advection-Dispersion Equation. Under the assumption that the solution is nonsmooth at the initial time, we…