In this paper, numerical solution of two points 2 order nonlinear boundary-value problems was considered. The numerical solution was reviewed with nonlinear shooting method, finite-difference method and fourth order compact method. The results were compared to check the accuracy of numerical schemes with exact solution. It was found that the nonlinear shooting method is more accurate than finit...

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 ...

Fourth-order combined compact finite difference scheme is given for solving the time fractional convection–diffusion–reaction equation with variable coefficients. We introduce the flux as a new variable and transform the original equation into a system of two equations. Compact difference is used as a high-order approximation for spatial derivatives of integer order in the coupled partial diffe...

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...