Related papers: Structure-Preserving Numerical Methods for Fokker-…
Positivity preservation of key physical quantities in the context of fluid flows, such as density and internal energy, is an essential property of a numerical scheme as otherwise the solution lacks physical relevance and has a not…
Patankar-type schemes are linearly implicit time integration methods designed to be unconditionally positivity-preserving. However, there are only little results on their stability or robustness. We suggest two approaches to analyze the…
A numerical solution to the Fokker-Planck equation using a two-level scheme is presented. The Fokker-Planck (FP) equation is of parabolic type equation govern the time evolution of probability density function of the stochastic processes.…
We study two schemes for a time-fractional Fokker-Planck equation with space- and time-dependent forcing in one space dimension. The first scheme is continuous in time and is discretized in space using a piecewise-linear Galerkin finite…
In this work, we develop novel structure-preserving numerical schemes for a class of nonlinear Fokker--Planck equations with nonlocal interactions. Such equations can cover many cases of importance, such as porous medium equations with…
For quantum computers to become useful tools to physicists, engineers and computational scientists, quantum algorithms for solving nonlinear differential equations need to be developed. Despite recent advances, the quest for a solver that…
The Fokker-Planck (FP) model is one of the commonly used methods for studies of the dynamical evolution of dense spherical stellar systems such as globular clusters and galactic nuclei. The FP model is numerically stable in most cases, but…
This paper explores the use of a discrete singular convolution algorithm as a unified approach for numerical integration of the Fokker-Planck equation. The unified features of the discrete singular convolution algorithm are discussed. It is…
In this paper we focus on the construction of numerical schemes for nonlinear Fokker-Planck equations that preserve the structural properties, like non negativity of the solution, entropy dissipation and large time behavior. The methods…
An implicit and conservative numerical scheme is proposed for the isotropic quantum Fokker-Planck equation describing the evolution of degenerate electrons subject to elastic collisions with other electrons and ions. The electron-ion and…
In this paper we present a direct perturbative method to solving certain Fokker-Planck equations, which have constant diffusion coefficients and some small parameters in the drift coefficients. The method makes use of the connection between…
In this work, we are concerned with the Fokker-Planck equations associated with the Nonlinear Noisy Leaky Integrate-and-Fire model for neuron networks. Due to the jump mechanism at the microscopic level, such Fokker-Planck equations are…
Many low-Mach or all-Mach number codes are based on space discretizations which in combination with the first order explicit Euler method as time integration would lead to an unstable scheme. In this paper, we investigate how the choice of…
In this paper, we introduce second order and fourth order space discretization via finite difference implementation of the finite element method for solving Fokker-Planck equations associated with irreversible processes. The proposed…
For high-order accurate schemes such as discontinuous Galerkin (DG) methods solving Fokker-Planck equations, it is desired to efficiently enforce positivity without losing conservation and high-order accuracy, especially for implicit time…
In the present article, an approach to find the exact solution of the fractional Fokker-Planck equation is presented. It is based on transforming it to a system of first-order partial differential equation via Hopf transformation, together…
Ion transport, often described by the Poisson--Nernst--Planck (PNP) equations, is ubiquitous in electrochemical devices and many biological processes of significance. In this work, we develop conservative, positivity-preserving, energy…
In this paper we study some properties of the generalized Fokker-Planck equation induced by the time-changed fractional Ornstein-Uhlenbeck process. First of all, we exploit some sufficient conditions to show that a mild solution of such…
We perform a numerical approximation of coherent sets in finite-dimensional smooth dynamical systems by computing singular vectors of the transfer operator for a stochastically perturbed flow. This operator is obtained by solution of a…
The time-fractional Fokker-Planck equation is a key model for characterizing anomalous diffusion, stochastic transport, and non-equilibrium statistical mechanics with applications in finance, chaotic dynamics, optical physics, and…