In this paper, a numerical solution of time fractional advection-dispersion equations are presented.The new implicit nite dierence methods for solving these equations are studied. We examinepractical numerical methods to solve a class of initial-boundary value fractional partial dierentialequations with variable coecients on a nite domain. Stability, consistency, and (therefore) convergenceof t...

We consider a fully discrete approximation of the H gradient flow of an energy integral where the energy density is given by the sum of a nonnegative multi-well potential term and a bending energy term. The spatial discretization is based on a Fourier spectral method, which is combined with an implicit Euler time discretization. The numerical method is shown to be stable and to exhibit optimal ...

A new method for the numerical simulation of the so-called soliton dynamics arising in a nonlinear Schrödinger equation in the semi-classical regime is proposed. For the time discretization a classical fourth-order splitting method is used. For the spatial discretization, however, a meshfree method is employed in contrast to the usual choice of (pseudo) spectral methods. This approach allows to...

We present a new wavelet numerical scheme for the discretization of Navier-Stokes equations with physical boundary conditions. The temporal discretization of the method is inspired from the projection method. Helmholtz-Hodge decomposition using divergence-free and curl-free wavelet bases satisfying physical boundary conditions allows to define the projection operator. This avoids the use of Poi...

We present a new wavelet numerical scheme for the discretization of Navier-Stokes equations with physical boundary conditions. The temporal discretization of the method is inspired from the projection method. Helmholtz-Hodge decomposition using divergence-free and curl-free wavelet bases satisfying physical boundary conditions allows to define the projection operator. This avoids the use of Poi...

Abstract. We consider a parabolic interface problem which models the transport of a dissolved species in two-phase incompressible flow problems. Due to the so-called Henry interface condition the solution is discontinuous across the interface. We use an extended finite element space combined with a method due to Nitsche for the spatial discretization of this problem and derive optimal discretiz...

We investigate a new numerical approach for the computation of the threedimensional flow in a discrete fracture network that does not require a conforming discretization of partial differential equations on complex three-dimensional systems of planar fractures. The discretization within each fracture is performed independently of the discretization of the other fractures and of their intersecti...

Compact finite difference scheme is applied for a partial integro-differential equation with a weakly singular kernel. The product trapezoidal method is applied for discretization of the integral term. The order of accuracy in space and time is , where . Stability and convergence in  norm are discussed through energy method. Numerical examples are provided to confirm the theoretical prediction ...

Discretization is an important preprocessing technique in data mining tasks. Univariate Discretization is the most commonly used method. It discretizes only one single attribute of a dataset at a time, without considering the interaction information with other attributes. Since it is multi-attribute rather than one single attribute determines the targeted class attribute, the result of Univaria...

In this article, we propose optimal discretization of analog filters (or controllers) based on the theory of sampled-data H∞ control. We formulate the discretization problem as minimization of the H∞ norm of the error system between a (delayed) target analog filter and a digital system including an ideal sampler, a zero-order hold, and a digital filter. The problem is reduced to discrete-time H...