We give a unified method to derive the strong convergence rate of backward Euler scheme for monotone SDEs in $L^p(\Omega)$-norm, with general $p \ge 4$. The results are applied SODEs polynomial growth coefficients. also generalize argument Galerkin-based SPDEs coefficients driven by multiplicative trace-class noise.

This is a continuation of the first author’s earlier paper [17] jointly with Pang and Deng, in which the authors established some sufficient conditions under which the Euler–Maruyama (EM) method can reproduce the almost sure exponential stability of the test hybrid SDEs. The key condition imposed in [17] is the global Lipschitz condition. However, we will show in this paper that without this gl...

Abstract In this paper, we study the existence and uniqueness of random periodic solution for a stochastic differential equation with one-sided Lipschitz condition (also known as monotonicity condition) convergence its numerical approximation via backward Euler–Maruyama method. The is shown limit pull-back flows SDE discretized SDE, respectively. We establish rate strong error method order 1/2.

Abstract. In this paper, the author propose a numerical method to compute the solution of the Cauchy problem: wt − (w m wx)x = w , the initial condition is a nonnegative function with compact support, m > 0, 1 < p < m + 1. The problem is split in two parts: A hyperbolic term solved by using the Hopf and Lax formula and a parabolic term solved by a backward linearized Euler method in time and a ...

There are three important steps in the proof the BDF theorem for essentially normal operators having essential spectrum X ⊆ C. (1) Ext(X) has a neutral element. (2) Ext(X) is a group (i.e., has inverses). (3) Ext(X) depends only on the homotopy class of X. In this lecture we will exhibit the neutral element of Ext(X) and describe the generalization of that result to noncommutative C∗-algebras (...

The large time behavior of entropy solution to the compressible Euler equations for polytropic gas (the pressure $p(\rho)=\kappa\rho^{\gamma}, \gamma>1$) with dependent damping like $-\frac{1}{(1+t)^\lambda}\rho u$ ($0<\lambda<1$) is investigated. By introducing an elaborate iterative method and using intensive analysis, it proved that $L^\infty$ finite initial mass converges strongly in natura...

We study the linear stability of the fifth-order Weighted Essentially Non-Oscillatory spatial discretization (WENO5) combined with explicit time stepping applied to the one-dimensional advection equation. We show that it is not necessary for the stability domain of the time integrator to include a part of the imaginary axis. In particular, we show that the combination of WENO5 with either the f...

In this talk, we will introduce high accurate numerical schemes for solving forward backward stochastic differential equations (FBSDEs) with jumps. In these schemes, the simplest Euler scheme with only one jump is used to solve the forward stochastic differential equation (SDE), and multistep schemes is used to solve the backward stochastic differential equation (BSDE) with high convergence rat...

We consider the simulation of a system decoupled forward–backward stochastic differential equations (FBSDEs) driven by pure jump Lévy process L and an independent Brownian motion B . allow to have infinite activity. Therefore, it is necessary for employ finite approximation its measure. use generalized shot noise series representation method [26] approximate driving compute p error, ≥ 2, betwee...