A Numerical Method For Space Fractional Diffusion Equations Using A Semi-disrete Scheme And Chebyshev Collocation Method

Abstract

In the present paper, a numerical approach to efficiently calculate the solution of space fractional diffusion equations is investigated. The finite difference scheme and Chebyshev collocation method is applied to solve this problems. Also, the matrix form of the proposed method is obtained. The numerical examples and comparison with other methods shows that the present method is effective.

Numerical approach for solving space fractional orderdiffusion equations using shifted Chebyshev polynomials of the fourth kind

“…It has been used in modeling turbulent flow [10], groundwater contaminant transport [4], chaotic dynamics of classical conservative systems [28,45], applications in biology [16], and applications in other fields [5,12,21,33]. Later there appeared several numerical methods for solving fractional diffusion equations, such as those in [2,3,21,22] where the authors used the finite difference method. Cui [11] and Geo and Sun [17] used the compact finite difference scheme.…”

Adomian Decomposition Method For Solving Fractional Bratu-type Equations

“…Therefore several methods for the approximate solutions to classical differential equations [11] are extended to solve differential equations of fractional order numerically. These methods include, Adomian decomposition method [12], homotopy perturbation method [13][14][15][16], homotopy analysis method [17], variational iteration method [18], generalized differential transform method [19], finite difference method [20] and etc [21,22].…”

The Chebyshev collocation solution of the time fractional coupled Burgers' equation

“…The well-known Chebyshev polynomial of the first kind of degree n, which are defined on interval [−1, 1] are given by [5]:…”

“…This type of differentiation and integration could be considered as generalization to the usual definition of differentiation and integration to non-integer order [1,3,4]. Fractional partial differential equations have recently been applied to different areas of sciences, mathematics, physics, chemistry, engineering, continuum, statistical mechanics, and dynamic system [2,5,8,14,23,29,33,34].…”