Multigrid schemes for high order finite difference methods on summationby-parts form are studied by comparing the effect of different interpolation operators. By using the standard linear prolongation and restriction operators, the Galerkin condition leads to inaccurate coarse grid discretizations. In this paper, an alternative class of interpolation operators that bypass this issue and preserv...

Article history: Received 27 June 2013 Received in revised form 22 January 2014 Accepted 25 March 2014 Available online 2 April 2014

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 ...

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 ...