Based on the concept of alternating group and domain decomposition, we present a class of alternating group explicit-implicit method and an alternating group Crank-Nicolson method for solving convection-diffusion equation. Both of the two methods are effective in convection dominant cases. The concept of the construction of the methods is also be applied to 2D convection-diffusion equations. Nu...

The aim of this paper is to extend the split-step idea for the solution of fractional partial differential equations. We consider the multidimensional nonlinear Schr"{o}dinger equation with the Riesz space fractional derivative and propose an efficient numerical algorithm to obtain it's approximate solutions. To this end, we first discretize the Riesz fractional derivative then apply the Crank-...

mistreated (Isenberg-Grezda, Kutberg & Nicolson, 2012, Isenberg-Grezda; Chabon & Nicolson, 2014). There is a need for translational research in this field to connect “bench to bedside” in order to find the best ways to help patients with ARBD. Public health managers should take responsibility of such a relevant issue, as many of these patients are at the boundaries of different medical speciali...

This paper formulates and analyzes a weak solution to the coupling of time-dependent Navier-Stokes flow with Darcy flow under certain boundary conditions, one of them being the Beaver-Joseph-Saffman law on the interface. Existence and a priori estimates for the weak solution are shown under additional regularity assumptions. We introduce a fully discrete scheme with the unknowns being the Navie...

The aim of the present paper is to present a numerical algorithm for the time-dependent generalized regularized long wave equation with boundary conditions. We semi-discretize the continuous problem by means of the Crank–Nicolson finite difference method in the temporal direction and exponential B-spline collocation method in the spatial direction. The method is shown to be unconditionally stab...

In this paper, a new alternating direction implicit Galerkin–Legendre spectral method for the two-dimensional Riesz space fractional nonlinear reaction-diffusion equation is developed. The temporal component is discretized by the Crank–Nicolson method. The detailed implementation of the method is presented. The stability and convergence analysis is strictly proven, which shows that the derived ...

A simulation model of the human body is developed in frequency dependent Crank Nicolson finite difference time domain (FD-CN-FDTD) method. Numerical simulation of electromagnetic wave propagation inside the human head is presented. Advantages of using time discretization beyond the Courant Friedrich-Lewy (CFL) limit in FD-CN-FDTD method are shown. Parallelization using Open Multi-Processing (Op...