Related papers: A more accurate numerical scheme for diffusive sho…
Particle acceleration in collisionless astrophysical shocks, i.e., diffusive shock acceleration (DSA), is the most likely mechanism for producing cosmic rays, at least below 10^{15} eV. Despite the success of this theory, several key…
Diffusion approximation provides weak approximation for stochastic gradient descent algorithms in a finite time horizon. In this paper, we introduce new tools motivated by the backward error analysis of numerical stochastic differential…
We discuss a numerical scheme to solve the continuum Kardar-Parisi-Zhang equation in generic spatial dimensions. It is based on a momentum-space discretization of the continuum equation and on a pseudo-spectral approximation of the…
In this paper, we develop and analyze a stochastic algorithm for solving space-time fractional diffusion models, which are widely used to describe anomalous diffusion dynamics. These models pose substantial numerical challenges due to the…
The Equation-Free approach to efficient multiscale numerical computation marries trusted micro-scale simulations to a framework for numerical macro-scale reduction -- the patch dynamics scheme. A recent novel patch scheme empowered the…
This paper compares the HLLEM and HLL-CPS schemes for Euler equations and proposes improvements for all Mach number flows. Enhancements to the HLLEM scheme involve adding anti-diffusion terms in the face normal direction and modifying…
We study asymptotic error distributions associated with standard approximation scheme for one-dimensional stochastic differential equations driven by fractional Brownian motions. This problem was studied by, for instance, Gradinaru-Nourdin…
We present an implicit Split-Step explicit Euler type Method (dubbed SSM) for the simulation of McKean-Vlasov Stochastic Differential Equations (MV-SDEs) with drifts of superlinear growth in space, Lipschitz in measure and non-constant…
Nowadays, the calculation of the Galactic Cosmic Rays diffusion coefficient with direct microscopic numerical simulations is a widespread approach. In this work, we investigated the numerical limits for such calculations and demonstrated…
Using Stokesian dynamics simulations, we examine the flow of a monodisperse, neutrally buoyant, homogeneous suspension of non-Brownian solid spheres in simple shear, starting from a large number of independent hard-sphere distributions and…
Stationary solutions to the equations of non-linear diffusive shock acceleration play a fundamental role in the theory of cosmic-ray acceleration. Their existence usually requires that a fraction of the accelerated particles be allowed to…
When solving partial differential equations using classical schemes such as finite difference or finite volume methods, sufficiently fine meshes and carefully designed schemes are required to achieve high-order accuracy of numerical…
This paper presents and analyzes the compensated projected Euler-Maruyama method for stochastic differential equations with jumps under a global monotonicity condition. Compared with existing conditions, this condition allows the…
We propose a straightforward and effective method for discretizing multi-dimensional diffusion processes as an extension of Milstein scheme. The new scheme is explicitly given and can be simulated using Gaussian variates, requiring the same…
In this article, we consider numerical schemes for polynomial diffusions on the unit ball, which are solutions of stochastic differential equations with a diffusion coefficient of the form $\sqrt{1-|x|^{2}}$. We introduce a semi-implicit…
We model the diffusive shock acceleration of particles in a system of two colliding shock waves and present a method to solve the time-dependent problem analytically in the test-particle approximation and high energy limit. In particular,…
In this paper we focus on a discrete physical model describing granular crystals, whose equations of motion can be described by a system of differential difference equations (DDEs). After revisiting earlier continuum approximations, we…
This work develops Monte Carlo Euler adaptive time stepping methods for the weak approximation problem of jump diffusion driven stochastic differential equations. The main result is the derivation of a new expansion for the omputational…
Gaseous flows show a diverse set of behaviors on different characteristic scales. Given the coarse-grained modeling in theories of fluids, considerable uncertainties may exist between the flow-field solutions and the real physics. To study…
A discretization scheme is introduced for a set of convection-diffusion equations with a non-linear reaction term, where the convection velocity is constant for each reactant. This constancy allows a transformation to new spatial variables,…