Solutions of a boundary value problem for the Korteweg–de Vries equation are approximated numerically using a finite-difference method, and a collocation method based on Chebyshev polynomials. The performance of the two methods is compared using exact solutions that are exponentially small at the boundaries. The Chebyshev method is found to be more efficient. © 2009 IMACS. Published by Elsevier...

In this paper, we give sixth order compact finite difference formula for second order integro-differential equations (IDE) with different boundary conditions, and both of error estimates and numerical experiments confirm our compact finite difference method can get fifth order of accuracy. We also adjust compact finite difference method for first order IDE and a system of IDE and give numerical...

We numerically investigate the electric potential distribution over a twodimensional continuum percolation model between the electrodes. The model consists of overlapped conductive particles on the background with an infinitesimal conductivity. Using the finite difference method, we solve the generalized Laplace equation and show that in the potential distribution, there appear the quasi-equipo...

We study Soret-Dufour and radiation effects on unsteady viscous incompressible MHD flow along semi infinite inclined permeable moving plate with variable temperature and mass diffusion embedded in a porous medium numerically, by taking into account the effect of viscous dissipation. The dimensionless governing equations of flow field are solved numerically by Crank-Nicolson finite difference me...

In this paper we propose a finite difference scheme for temporal discretization of the time-fractional thermistor problem, which is obtained from the so-called thermistor problem by replacing the first-order time derivative with a fractional derivative of order α (0 ≤ α ≤ 1). An existence result is established for the semidiscrete problem. Stability and error analysis are then provided, showing...

The main idea of this paper is to demonstrate a stochastic computational technique consisting of the generalized stochastic perturbation method using the Taylor expansions of random variables and the classical Finite Difference Method based on regular grids. As it is documented by computational illustrations, it is possible to determine, using this approach, also higher probabilistic moments fo...

We elucidate the dispersion behavior of deep-subwavelength propagating modes in coaxial plasmonic structures by making an explicit connection with the planar metal-insulator-metal geometry. We provide an intuitive picture that allows for a qualitative understanding and a quantitative prediction of the entire dispersion behavior, which includes the number of modes at every frequency, the modal p...

An unsteady, two-dimensional, hydro magnetic, laminar mixed convective boundarylayer flow of an incompressible, Newtonian, electrically-conducting and radiating fluid along a semi-infinite vertical permeable moving plate with heat and mass transfer is analyzed, by taking into account the effect of viscous dissipation. The plate moves with a constant velocity in the direction of fluid flow while...

Conservative linear equations arise in many areas of application, including continuum mechanics or high-frequency geometrical optics approximations. This kind of equation admits most of the time solutions which are only bounded measures in the space variable known as duality solutions. In this paper, we study the convergence of a class of finite-difference numerical schemes and introduce an app...