Related papers: Exponential integrability properties of numerical …
In this work we analyze the entropic properties of the Euler equations when the system is closed with the assumption of a polytropic gas. In this case, the pressure solely depends upon the density of the fluid and the energy equation is not…
We study a numerical approximation for a nonlinear variable-order fractional differential equation via an integral equation method. Due to the lack of the monotonicity of the discretization coefficients of the variable-order fractional…
In this paper, we introduce Mellin-Steklov exponential samplingoperators of order $r,r\in\mathbb{N}$, by considering appropriate Mellin-Steklov integrals. We investigate the approximation properties of these operators in continuousbounded…
This paper studies the convergence rate of the Euler-Maruyama scheme for systems of interacting particles used to approximate solutions of nonlinear Fokker-Planck equations with singular interaction kernels, such as the Keller-Segel model.…
Inspired by the truncated Euler-Maruyama method developed in Mao (J. Comput. Appl. Math. 2015), we propose the truncated Milstein method in this paper. The strong convergence rate is proved to be close to 1 for a class of highly non-linear…
An explicit numerical method is developed for a class of non-autonomous time-changed stochastic differential equations, whose coefficients obey H\"older's continuity in terms of the time variables and are allowed to grow super-linearly in…
The machine learning explosion has created a prominent trend in modern computer hardware towards low precision floating-point operations. In response, there have been growing efforts to use low and mixed precision in general scientific…
This paper presents the error analysis of numerical methods on graded meshes for stochastic Volterra equations with weakly singular kernels. We first prove a novel regularity estimate for the exact solution via analyzing the associated…
We investigate the long-time behavior of exact solutions and numerical approximations of linear stochastic evolution equations defined on the sphere. We focus on three classical models arising in mathematical physics: the stochastic wave…
We introduce a new concept of dissipative measure-valued martingale solutions to the stochastic compressible Euler equations. These solutions are weak in the probabilistic sense i.e., the probability space and the driving Wiener process are…
This work develops new results for stochastic approximation algorithms. The emphases are on treating algorithms and limits with discontinuities. The main ingredients include the use of differential inclusions, set-valued analysis, and…
This paper discusses new simulation algorithms for stochastic chemical kinetics that exploit the linearity of the chemical master equation and its matrix exponential exact solution. These algorithms make use of various approximations of the…
We propose and analyze the numerical approximation for a viscoelastic Euler-Bernoulli beam model containing a nonlinear strong damping coefficient. The finite difference method is used for spatial discretization, while the backward Euler…
A practical and accessible introduction to most probable phase portraits is given. The reader is assumed to be familiar with stochastic differential equations and Euler-Maruyama method in numerical simulation. The article first introduce…
Classical approximation results for stochastic differential equations analyze the $L^p$-distance between the exact solution and its Euler-Maruyama approximations. In this article we measure the error with temporal-spatial H\"older-norms.…
The backward Euler-Maruyama (BEM) method is employed to approximate the invariant measure of stochastic differential equations, where both the drift and the diffusion coefficient are allowed to grow super-linearly. The existence and…
We consider a class of stochastic path-dependent volatility models where the stochastic volatility, whose square follows the Cox-Ingersoll-Ross model, is multiplied by a (leverage) function of the spot price, its running maximum, and time.…
We study integrodifferential operators and regularity estimates for solutions to integrodifferential equations. Our emphasis is on kernels with a critically low singularity which does not allow for standard scaling. For example, we treat…
In this study, we consider a numerical implementation of the nonlinear Rosenbluth-Trubnikov collision operator for particle simulations in plasma physics in the framework of the finite element method (FEM). The relevant particle evolution…
We consider the long-time behavior of an explicit tamed exponential Euler scheme applied to a class of parabolic semilinear stochastic partial differential equations driven by additive noise, under a one-sided Lipschitz continuity…