In this study we propose a space and time-accurate numerical method for Korteweg– de Vries equation. In deriving the computational scheme, Taylor generalized Euler time discretization is performed prior to wavelet based Galerkin spatial approximation. This leads to the implicit system which can also be solved by explicit algorithms. Korteweg– de Vries equation is also solved by a operator split...

We propose a two-dimensional asymptotic-preserving scheme for linear transport equations with diffusive scalings. It is an extension of the time splitting developed by Jin, Pareschi and Toscani [19], but uses spatial discretizations on staggered grids, which preserves the discrete diffusion limit with a more compact stencil. The first novelty of this paper is that we propose a staggering in 2D ...

The simulation of chemically reacting ows in speci c situations is a basic instrument in natural sciences in order to understand complex phenomena (e.g., salt concentrations in oceans) as well as in engineering sciences (e.g., the optimization of the Czochralski growth in semiconductor industries, see e.g. [7, 15]). The objective of the paper is two-fold: First, we will present a rst-order time...

We propose a quasi-Monte Carlo (QMC) scheme for the simulation of the general dynamics equation (GDE) for aerosols. The mass distribution is approximated by a fixed number of weighted numerical particles. Time is discretized and a splitting approach is used. Coagulation is simulated with a stochastic particle method using quasi-random points. In addition, the particles are reordered by increasi...

A full discrete two-level postprocessing Fourier Galerkin scheme for the unsteady Navier-Stokes equations with periodic boundary conditions is proposed in this talk. By defining a new projection, the interaction between the large and small eddies is reflected by the associated space splitting to some extent. Then a weakly coupled system of the large and small eddies is obtained. Stability and e...

We study a finite element approximation for the consistent splitting scheme proposed in [11] for the time dependent Navier-Stokes equations. At each time step, we only need to solve a Poisson type equation for each component of the velocity and the pressure. We cast the finite element approximation in an abstract form using appropriately defined discrete differential operators, and derive optim...

In this paper we propose an explicit two-level conservative scheme based on a TE/TM like splitting of the field components in time. Its dispersion properties are adjusted to accelerator problems. It is simpler and faster than the implicit version [1]. It does not have dispersion in the longitudinal direction and the dispersion properties in the transversal plane are improved. The explicit chara...

Iterative splitting methods have a huge amount to compute matrix exponential. Here, the acceleration and recovering of higher-order schemes can be achieved. From a theoretical point of view, iterative splitting methods are at least alternating Picards fix-point iteration schemes. For practical applications, it is important to compute very fast matrix exponentials. In this paper, we concentrate ...

in this paper, a numerical efficient method is proposed for the solution of time fractionalmobile/immobile equation. the fractional derivative of equation is described in the caputosense. the proposed method is based on a finite difference scheme in time and legendrespectral method in space. in this approach the time fractional derivative of mentioned equationis approximated by a scheme of order o...