A space-time spectral collocation algorithm for the variable order fractional wave equation

作者：Bhrawy A H^*; Doha E H; Alzaidy J F; Abdelkawy M A

来源：SpringerPlus, 2016, 5(1): 1220.

DOI：10.1186/s40064-016-2899-5

• Variable-order fractional derivative
• Collocation method
• Jacobi polynomials
• Gauss quadrature
• Fractional wave equation

The variable order wave equation plays a major role in acoustics, electromagnetics, and fluid dynamics. In this paper, we consider the space-time variable order fractional wave equation with variable coefficients. We propose an effective numerical method for solving the aforementioned problem in a bounded domain. The shifted Jacobi polynomials are used as basis functions, and the variable-order fractional derivative is described in the Caputo sense. The proposed method is a combination of shifted Jacobi-Gauss-Lobatto collocation scheme for the spatial discretization and the shifted Jacobi-Gauss-Radau collocation scheme for temporal discretization. The aforementioned problem is then reduced to a problem consists of a system of easily solvable algebraic equations. Finally, numerical examples are presented to show the effectiveness of the proposed numerical method.

• 出版日期2016-8-2