It is well known that the strong error approximation, in the space of continuous paths equipped with the supremum norm, between a diffusion process, with smooth coefficients, and its Euler approximation with step $1/n$ is $O(nˆ{-1/2})$ and that the weak error estimation between the marginal laws, at the terminal time $T$, is $O(nˆ{-1})$. In this talk, we study the $p-$Wasserstein distance betwe...

This paper establishes a link between the stability of a first order, explicit discrete event integration scheme and the stability criteria for the explicit Euler method. The paper begins by constructing a time-varying linear system with bounded inputs that is equivalent to the first order discrete event integration scheme. The stability of the discrete event system is shown to result from the ...

We establish general moment estimates for the discrete and continuous exit times of a general Itô process in terms of the distance to the boundary. These estimates serve as intermediate steps to obtain strong convergence results for the approximation of a continuous exit time by a discrete counterpart, computed on a grid. In particular, we prove that the discrete exit time of the Euler scheme o...

We show that there are ordinary differential equations in R with unbounded solutions, for which the difference equations obtained by using the forward Euler method have all solutions bounded.

A fast, accurate method for solving the Euler equations will be described. A new mesh generation scheme, capable of creating a mesh around winglbodyltail-plane/fin combinations will also be presented. The paper concludes with a proliminary result demonstrating how the Euler method performs for a typical aircraft configuration.

A new variant of Local Linearization (LL) method is proposed for the numerical (strong) solution of differential equations driven by (additive) alpha-stable Lévy motions. This is studied through simulations making emphasis in comparison with the Euler method from the viewpoint of numerical stability. In particular, a number of examples of stiff equations are shown in which the Euler method has ...

This paper considers the Euler tour of an uncertain random graph, in which some edges exist with some degrees in uncertain measure and others exist with some degrees in probability measure. The concept of Euler index of an uncertain random graph is proposed first, and then a method to calculate the Euler index of an uncertain random graph is given. In addition, some properties of the Euler inde...

an_eul is a new automatic method for simultaneous approximation of location, depth, and structural index (geometry) of magnetic sources. in the 2d case analytic signal is defined as a conjugate function whose imaginary part is the hilbert transform of its real part. since the first vertical derivative of the magnetic field is the hilbert transform of its horizontal derivative, vertical and hori...

In this paper, we consider reinitializing level functions through equation /tþ sgnð/Þðkr/k 1Þ 1⁄4 0 [16]. The method of Russo and Smereka [11] is taken in the spatial discretization of the equation. The spatial discretization is, simply speaking, the second order ENO finite difference with subcell resolution near the interface. Our main interest is on the temporal discretization of the equation...

We present and analyse two implicit methods for Ito stochastic differential equations (SDEs) with Poisson-driven jumps. The first method, SSBE, is a split-step extension of the backward Euler method. The second method, CSSBE, arises from the introduction of a compensated, martingale, form of the Poisson process. We show that both methods are amenable to rigorous analysis when a one-sided Lipsch...