Fractional-order diffusion equations are viewed as generalizations of classical diffusion equations, treating super-diffusive flow processes. In this paper, in order to solve the fractional advection-diffusion equation, the fractional characteristic finite difference method is presented, which is based on the method of characteristics (MOC) and fractional finite difference (FD) procedures. The ...

in chemical engineering, several processes are represented by singular boundary value problems. in general, classical numerical methods fail to produce good approximations for the singular boundary value problems. in this paper, chebyshev finite difference (chfd) method and dtm-pad´e method, which is a combination of differential transform method (dtm) and pad´e approximant, are applied for sol...

Using classic differential quadrature formulae and uniform grids, this paper systematically constructs a variety of high-order finite difference schemes, and some of these schemes are consistent with the so-called boundary value methods. The derived difference schemes enjoy the same stability and accuracy properties with correspondent differential quadrature methods but have a simpler form of c...

High-order finite difference methods are efficient, easy to program, scale well in multiple dimensions and can be modified locally for various reasons (such as shock treatment for example). The main drawback has been the complicated and sometimes even mysterious stability treatment at boundaries and interfaces required for a stable scheme. The research on summation-byparts operators and weak bo...

and Applied Analysis 3 The grid function y(x, t) is a function defined at the grid points of g. we denote the nodal values of a grid function y(x, t) between time levels t 0 and t 0 as y (x, t) = y (x 1 , x 2 , t l,j i ) = y l,j n1 ,n2 , (11) for x ∈ ω i , i > 0, j = 0, . . . , m i . For x ∈ ω 0 we define y (x, t) = y (x 1 , x 2 , t l+1 0 ) = y l+1 n1 ,n2 . (12) δ x1 , δ x1 and δ x2 , δ x2 are ...

This paper deals with the development of a computer model for flood routing in narrow rivers. Equations describing the propagation of a flood wave in a channel-flood plain system are presented and solved using an implicit finite difference scheme. Particular emphasis has been given to the treatment of the friction term in the governing equation of motion.

In this article a modification of the Chebyshev collocation method is applied to the solution of space fractional differential equations.The fractional derivative is considered in the Caputo sense.The finite difference scheme and Chebyshev collocation method are used .The numerical results obtained by this way have been compared with other methods.The results show the reliability and efficiency...

In this paper, we improve b-spline collocation method for Benjamin-Bona-Mahony-Burgers (BBMB) by using defect correction principle. The exact finite difference scheme is used to find defect and the defect correction principle is used to improve collocation method. The method is tested on somemodel problems and the numerical results have been obtained and compared.

This paper presents a family of finite difference schemes for the first and second derivatives of smooth functions. The schemes are Hermitian and symmetric and may be considered a more general version of the standard compact (Padé) schemes discussed by Lele. They are different from the standard Padé schemes, in that the first and second derivatives are evaluated simultaneously. For the same ste...