A wavelet approach for the multi-term time fractional diffusion-wave equation

ABSTRACT

In this paper, a Galerkin method based on the second kind Chebyshev wavelets (SKCWs) is established for solving the multi-term time fractional diffusion-wave equation. To do this, a new operational matrix of fractional integration for the SKCWs must be derived and in order to improve the computational efficiency, the hat functions are proposed to create a general procedure for constructing this matrix. Implementation of these wavelet basis functions and their operational matrix of fractional integration simplifies the problem under consideration to a system of linear algebraic equations, which greatly decreases the computational cost for finding an approximate solution. The main privilege of the proposed method is adjusting the initial and boundary conditions in the final system automatically. Theoretical error and convergence analysis of the SKCWs expansion approve the reliability of the approach. Also, numerical investigation reveals the applicability and accuracy of the presented method.

KEYWORDS:

• Multi-term time fractional diffusion-wave equation
• second kind Chebyshev wavelets
• hat functions
• operational matrix of fractional integration
• convergence analysis
• error analysis

2010 AMS SUBJECT CLASSIFICATIONS:

• 26A33
• 35R11

Disclosure statement

No potential conflict of interest was reported by the authors.