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In this paper, we propose a numerical scheme to solve space fractional order diffusion equation. Our scheme uses shifted Chebyshev polynomials of the third kind. The fractional differential derivatives are expressed in terms of the Caputo sense. Moreover, Chebyshev collocation method together with the finite difference method are used to reduce these types of differential equations to a system of algebraic equations which can be solved numerically. Numerical approximations performed by the proposed method are presented and compared with the results obtained by other numerical methods. The results reveal that our method is a simple and effective numerical method. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a class of finite difference method for solving two-sided space-fractional wave equation is considered. The stability and consistency of the method are discussed by means of Gerschgorin theorem and using the stability matrix analysis. Numerical solutions of some wave fractional partial differential equation models are presented. The results obtained are compared to exact solutions. [ABSTRACT FROM AUTHOR]

In this paper, the sufficient conditions that guarantee the convergence of the variational iteration method when applied to solve a coupled system of nonlinear partial differential equations are presented. Especial attention is given to the error bound of the nth term of the resultant sequence. Numerical examples to show the efficiency of the method are presented. [ABSTRACT FROM AUTHOR]

Abstract: In this Letter, we implement the variational iteration method and the homotopy perturbation method, for solving the system of fraction differential equations (FDE) generated by a multi-order fraction differential equation. The fractional derivatives are described in the Caputo sense. In these schemes, the solution takes the form of a convergent series with easily computable components. Numerical results show that the two approaches are easy to implement and accurate when applied to partial differential equations of fractional order. An algorithm to convert a multi-order FDE has been suggested which is valid in the most general cases. [Copyright &y& Elsevier]

Abstract: The variational iteration method is applied to solve the cubic nonlinear Schrödinger (CNLS) equation in one and two space variables. In both cases, we will reduce the CNLS equation to a coupled system of nonlinear equations. Numerical experiments are made to verify the efficiency of the method. Comparison with the theoretical solution shows that the variational iteration method is of high accuracy. [Copyright &y& Elsevier]

Abstract: This paper applies the variational iteration method and Adomian''s decomposition method to solve numerically the harmonic wave generation in a nonlinear, one-dimensional elastic half-space model subjected initially to a prescribed harmonic displacement. The results show that the variational iteration method is much easier, more convenient, and more stable and efficient than Adomian decomposition method. [Copyright &y& Elsevier]