We study effects of finite height and surrounding material on photonic crystal slabs of oneand two-dimensional photonic crystals with a pseudo-spectral method and finite difference time domain simulation methods. The band gap is shown to be strongly modified by the boundary material. As an application we suggest reflection and guiding of light by patterning the material on top/below the slab.

A technique to incorporate directivity in the Pseudospectral time-domain method (PSTD) for auralization purposes is presented. The Pseudospectral time-domain method is a numerical method for solving the wave equation that requires only two spatial points per wavelength, making it more efficient compared to other wave based methods. The effect of source directivity as well as the head-related di...

This paper is devoted with numerical solution of the system fractional differential equations (FDEs) which are generated by optimization problem using the Chebyshev collocation method. The fractional derivatives are presented in terms of Caputo sense. The application of the proposed method to the generated system of FDEs leads to algebraic system which can be solved by the Newton iteration meth...

Taking the axial heat conduction of wax deposition layer into account, a two-dimensional heat transfer model of calculating the temperature profile inside wax deposition layer was deduced and established based on the energy balance equation, the finite difference method was used to solve this model, and the influence of axial heat conduction on the distribution law of temperature profile inside...

A Mathematica based program has been elaborated in order to determine the symmetry group of a finite difference equation. The package provides functions which enable us to solve the determining equations of the related Lie group.

In this article we discuss numerical scheme for the approximation of the Willmore flow of graphs. The scheme is based on the finite difference method. We improve the scheme we presented in [8, 7] which is based on combination of the forward and the backward finite differences. The new scheme approximates the Willmore flow by the central differences and as a result it better preserves symmetry o...

We investigate several existing interface procedures for finite difference methods applied to advection-diffusion problems. The accuracy, stiffness and reflecting properties of the various interface procedures are investigated. The analysis and numerical experiments show that there are only minor differences between the various methods once a proper parameter choice has been made.

To characterise the reflection properties of printed surfaces like FSS (Frequency Selective Surfaces) and EBG (Electromagnetic Band-Gap), it is standard to use a plane wave excitation, and then compare the phase of the incident and the reflected waves. Thus, the phase difference over the frequency can be obtained. Nevertheless, in most cases, only infinite size structures are considered. In thi...

We study a projection and upwind finite difference scheme for a combustion model problem. Convergence to weak solutions is proved under the Courant-Friedrichs-Lewy condition. More assumptions are given on the ignition temperature; then convergence to strong detonation wave solutions or to weak detonation wave solutions is proved.

The large-time behavior of solutions and finite difference approximations of the nonlinear integro-differential equation associated with the penetration of a magnetic field into a substance are studied. Asymptotic properties of solutions for the initial-boundary value problem with homogeneous Dirichlet boundary conditions is considered. The rates of convergence are given too. The convergence of...