in this paper, the reorganization of the denominator of the discrete derivative and nonlocal approximation of nonlinear terms are used in the design of nonstandard finite difference schemes (nsfds). numerical examples confirming then efficiency of schemes, for some differential equations are provided. in order toillustrate the accuracy of the new nsfds, the numerical results are compared with s...

Abstract. Differential algebraic equations have wide applications in the field of engineering and science where the mathematical models form the descriptor systems. Analysis and modeling of the solutions of such systems need to handle with the different equations related to the systems. A time-domain discretization, for example, finite difference, finite volume, etc., may lead to DAEs of descri...

A high-order compact finite difference scheme for a fully nonlinear parabolic differential equation is analyzed. The equation arises in the modeling of option prices in financial markets with transaction costs. It is shown that the finite difference solution converges locally uniformly to the unique viscosity solution of the continuous equation. The proof is based on a careful study of the disc...

The finite difference time domain (FDTD) method is widely used as a computational tool to simulate the electromagnetic wave propagation in biological tissues. When expressed in terms of Debye parameters, dispersive biological tissues dielectric properties can be efficiently incorporated into FDTD codes. In this paper, FDTD formulation with nonuniform grid is presented to simulate a dual medical...

Abstract—A realistic model of ground soil is developed for the electromagnetic simulation of Ground Penetrating Radar (GPR) systems. A three dimensional Finite Difference Time Domain (FDTD) algorithm is formulated to model dispersive media using N -term Debye permittivity function with static conductivity. The formulation of the algorithm is based on the concept of the Piecewise Linear Recursiv...

Introduced a new method for computing dispersive media using finite difference time domain method by employing the recursive convolution approach to evaluate the discrete time convolution of the electric field and the dielectric susceptibility function. The RC approach results in a fast and computationally efficient algorithm; however, the accuracy achieved is not generally as good as that obta...

Keywords: KP–BBM-II equations Crank–Nicholson method Finite difference scheme Convergence Stability a b s t r a c t In this paper, the finite difference method is employed to solve Kadomtsev–Petviashvili– Benjamin–Bona–Mahony II (KP–BBM-II) partial differential equations. The time and space variable are discretized by the Crank–Nicholson method and the central-difference scheme, respectively. T...

As mentioned in 1 , difference equations appear naturally as a discrete analogue and as a numerical solution of differential and delay differential equations having applications in various scientific branches, such as biology, ecology, physics, economy, technics, and sociology. The stability, asymptotic behavior, and periodic property of solutions to difference equations had been widely investi...

We consider boundary-value problems for differential-difference equations containing incommensurable shifts of arguments in higher-order terms. prove that the case finite orbits boundary points generated by set difference operator, original problem is reduced to a differential equation with nonlocal conditions.