title: A space-time spectral collocation algorithm for the variable order fractional wave equation.
abstract: 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.
authors.affiliation: Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt.
authors.forename: A H
authors.initials: AH
authors.lastname: Bhrawy
authors.affiliation: Department of Mathematics, Faculty of Science, Cairo University, Giza, 12613 Egypt.
authors.forename: E H
authors.initials: EH
authors.lastname: Doha
authors.affiliation: Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia.
authors.forename: J F
authors.initials: JF
authors.lastname: Alzaidy
authors.affiliation: Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt ; Department of Mathematics and Statistics, College of Science, Al-Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia.
authors.forename: M A
authors.initials: MA
authors.lastname: Abdelkawy
keywords: Collocation method; Fractional wave equation; Gauss quadrature; Jacobi polynomials; Variable-order fractional derivative