This article is devoted to the numerical study of various finite difference approximations to the stochastic Burgers equation. Of particular interest in the one-dimensional case is the situation where the driving noise is white both in space and in time. We demonstrate that in this case, different finite difference schemes converge to different limiting processes as the mesh size tends to zero....

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In this paper we propose a new method based on adjoint systems for parametric sensitivity analysis of DAE’s. This method is employed in a series of experiments, and the results are compared with the estimation of sensitivity by a finite differences method, widely used because of the simplicity of its implementation. In addition, we propose a method extension based on the use of estimation funct...

This article presents a Monte Carlo methodology for solving the stochastic optimal timber harvest problem modeled as a recurrent American call option. A detailed description of the proposed methodology is given, and the Monte Carlo technique is contrasted with finite difference methods typically used to find solutions of the optimal harvest problem with stochastic prices. The use of the methodo...

A system of singularly perturbed ordinary differential equations of first order with given initial conditions is considered. The leading term of each equation is multiplied by a small positive parameter. These parameters are assumed to be distinct and they determine the different scales in the solution to this problem. A Shishkin piecewise–uniform mesh is constructed, which is used, in conjunct...

Three-dimensional model is established with finite difference method to simulate construction process based on design and construction plans of existing overpass pile foundation adjacent to certain large-section railway tunnel in Chengdu, China. Ground, isolation pile, main bridge pier and ramp pile near the tunnel are taken as research object, and surface settlement amount, displacement change...

In this article we introduce the multi-domain hybrid Spectral-WENO method aimed at the discontinuous solutions of hyperbolic conservation laws. The main idea is to conjugate the non-oscillatory properties of the high order weighted essentially non-oscillatory (WENO) finite difference schemes with the high computational efficiency and accuracy of spectral methods. Built in a multi-domain framewo...

An initial value problem with piecewise constant coefficients is considered. The accuracies for both finite difference methods and the pseudospectral method are analyzed, and a modification of the initial value problem is suggested. The modified problem is shown to have the same temporal period as the original problem does, and a second order accuracy is obtained for the pseudospectral method a...

This paper analyzes dielectric resonators using the FDTD method. Resonant frequencies and quality factors are calculated using Prony's method instead of the classical FFT

We introduce different high order time discretization schemes for backward semi-Lagrangian methods. These schemes are based on multi-step schemes like AdamsMoulton and Adams-Bashforth schemes combined with backward finite difference schemes. We apply these methods to transport equations for plasma physics applications and for the numerical simulation of instabilities in fluid mechanics. In the ...