title: Numerical solution of the one-dimensional fractional convection diffusion equations based on Chebyshev operational matrix.
abstract: In this paper, we are concerned with nonlinear one-dimensional fractional convection diffusion equations. An effective approach based on Chebyshev operational matrix is constructed to obtain the numerical solution of fractional convection diffusion equations with variable coefficients. The principal characteristic of the approach is the new orthogonal functions based on Chebyshev polynomials to the fractional calculus. The corresponding fractional differential operational matrix is derived. Then the matrix with the Tau method is utilized to transform the solution of this problem into the solution of a system of linear algebraic equations. By solving the linear algebraic equations, the numerical solution is obtained. The approach is tested via examples. It is shown that the proposed algorithm yields better results. Finally, error analysis shows that the algorithm is convergent.
authors: College of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan, 030024 Shanxi China.
authors: Jiaquan
authors: J
authors: Xie
authors: College of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan, 030024 Shanxi China.
authors: Qingxue
authors: Q
authors: Huang
authors: College of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan, 030024 Shanxi China.
authors: Xia
authors: X
authors: Yang
keywords: Chebyshev operational matrix; Numerical solution; One-dimensional fractional convection diffusion equations; Tau method; Variable coefficients