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 ...

The Goos-Hänchen shift on the surface when an optical beam is obliquely incident from one isotropic right-handed material (RHM) into another biaxial anisotropic left-handed material (BALHM) is numerically studied with the finite difference time domain (FDTD) method based on the Drude dispersive models. The analytical expression of the Goos-Hänchen shift is firstly presented, moreover the condit...

In atmospheric dynamics, the governing equations are usually non-linear partial differential equations. Some knowledge of finite-difference approximations to ordinary differential equations (especially first order) is needed, however. In fact, if we linearize a governing partial differential equation and assume a wave form for the solution, the equation simply reduces to an ordinary differentia...

Fractional order partial differential equations are generalizations of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initial- boundary value fractional partial differential equations with variable coefficients on a finite domain. S...

Numerical simulation of advective-dispersive contaminant transport is carried out by using high-order compact finite difference schemes combined with second-order MacCormack and fourth-order Runge-Kutta schemes. Both of the two schemes have accuracy of sixth-order in space. A sixth-order MacCormack scheme is proposed for the first time within this study. For the aim of demonstrating efficiency ...

In this paper we consider the matrix lattice equation Un,t(Un+1−Un−1)=g(n)I, in both its autonomous (g(n)=2) and nonautonomous (g(n)=2n−1) forms. We show that each of these two equations are integrable. addition, explore construction Miura maps which relate equations, via intermediate to analogs Volterra but dependent variables. For last systems, cases where variables belong certain special cla...