An efficient method based on the second kind Chebyshev wavelets for solving variable-order fractional convection diffusion equations

ABSTRACT

In this paper, a class of variable-order fractional convection diffusion equations have been solved with assistance of the second kind Chebyshev wavelets operational matrix. The operational matrix of variable-order fractional derivative is derived for the second kind Chebyshev wavelets. By implementing the second kind Chebyshev wavelets functions and also the associated operational matrix, the considered equations will be reduced to the corresponding Sylvester equation, which can be solved by some appropriate iterative solvers. Also, the convergence analysis of the proposed numerical method to the exact solutions and error estimation are given. A variety of numerical examples are considered to show the efficiency and accuracy of the presented technique.

KEYWORDS:

• Variable-order fractional convection diffusion equations
• the second kind Chebyshev wavelets
• operational matrix
• Sylvester equation
• convergence analysis

2010 AMS SUBJECT CLASSIFICATIONS:

• 65D15
• 65D30

Disclosure statement

No potential conflict of interest was reported by the authors.