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 ...

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...

In this paper, a novel variational approach for multi-modal image registration based on consistent non-rigid transforms is proposed. The forward and backward transforms are computed in a variational framework simultaneously. A consistency energy is added into the variational registration framework and an iterative method assures that the forward and backward transforms are close approximate inv...

A major problem in obtaining an efficient implementation of fully implicit RungeKutta (IRK) methods applied to systems of differential equations is to solve the underlying systems of nonlinear equations. Their solution is usually obtained by application of modified Newton iterations with an approximate Jacobian matrix. The systems of linear equations of the modified Newton method can actually b...

A major problem in obtaining an efficient implementation of fully implicit RungeKutta (IRK) methods applied to systems of differential equations is to solve the underlying systems of nonlinear equations. Their solution is usually obtained by application of modified Newton iterations with an approximate Jacobian matrix. The systems of linear equations of the modified Newton method can actually b...

After discretization in time with the implicit Euler method and in space with the Box method (c.f. [2]), we end up with a nonlinear system of equations. Newton’s method is used to solve these systems, where the required Jacobians are obtained by automatic differentiation (AD) (c.f. [3]). In contrast to approximate Jacobians via finite differences, AD gives exact Jacobians through a source code ...