In this study, we propose a numerical scheme for stochastic oscillators with additive noise obtained by the method of variation constants formula using generalized integrators. For both displacement and velocity components, show that has an order 3/2 in one step convergence first overall convergence. Theoretical statements are supported experiments.

We propose a simple fast spectral method for the Boltzmann collision operator with general collision kernels. In contrast to the direct spectral method [17, 27] which requires O(N) memory to store precomputed weights and has O(N) numerical complexity, the new method has complexity O(MN logN), where N is the number of discretization points in each of the three velocity dimensions and M is the to...

Numerical method for Cahn-Hilliard equation has been well-studied, but few can be generalized to fractional Cahn-Hilliard equation. In this project to modified the numerical method proposed by Brian Wetton et al in the paper High accuracy solutions to energy gradient flows from material science models[1]. The method they described in the paper is a pseudo-spectral method suitable for considerin...

A new time-discretization method for the development of a sampled-data representation of a nonlinear continuous-time input-driven system with time delay is proposed. It is based on the Taylor-Lie series expansion method and zero-order hold assumption. The mathematical structure of the new discretization scheme is explored and characterized as useful for establishing concrete connections between...

In the last years the interest in computer simulations of radioactive waste scenarios has increased. In this article we present numerical simulations with the software package TRAPRO. We consider a system of convection-diffusion-reaction-equations, that we coupled by their reaction terms. We present a new discretization method that improves the explicit discretization for the transportand react...

This paper deals with a method for the numerical solution of parabolic initialboundary value problems in two-dimensional polygonal domains Ω which are allowed to be non-convex. The Nitsche finite element method (as a mortar method) is applied for the discretization in space, i.e. non-matching meshes are used. For the discretization in time, the backward Euler method is employed. The rate of con...

We propose a simple fast spectral method for the Boltzmann collision operator with general collision kernels. In contrast to the direct spectral method [17, 28] which requires O(N) memory to store precomputed weights and has O(N) numerical complexity, the new method has complexity O(MN logN), where N is the number of discretization points in each of the three velocity dimensions and M is the to...

Abstract: We consider the anisotropic uniaxial formulation of the perfectly matched layer model (UPML). We prove the decay of different energies for the UPML, under certain assumptions, to demonstrate the well-posedness of this formulation. We present and analyze a mixed finite element method for the time domain discretization of the UPML to simulate wave propagation in unbounded domains in two...

The finite-difference time-domain method is a simple but powerful numerical method for simulating full-wave acoustic propagation and scattering. However, the method can demand a large amount of computational resources. Traditionally, continuously curved boundaries are represented in a stair-step fashion and thus accurately modeling scattering from a boundary will require a finer discretization ...

A semilinear parabolic problem of second order with an unknown solely time-dependent convolution kernel is considered. An additional given global measurement (a space integral of the solution) ensures the existence of a unique weak solution. The unknown kernel function can be approximated by a time-discrete numerical scheme based on Backward Euler’s method (Rothe’s method). In this contribution...