Numerical Approximation of space Fractional Order Wave Equation Using Shifted Chebyshev Polynomials of Second and third Kinds.

Abstract

In this paper,we proposed a numerical method to solve space fractional order wave equation (SFOWE). The method implements shifted Chebyshev polynomials of the second and third kinds with the fractional derivative interpreted in Caputo sense. Chebyshev collocation method is adopted to reduce the problem to a system of second order ordinary differential equation, while the finite difference method reduces that to a system of linear algebraic equations. The system of algebraic equations thus formed is solved with the aid of Mathematica 11.0. The proposed method gives results that compared favourably with existing results in the literature, while it is observed that the performance of second kind is relatively superior to that of the third kind polynomials. The results are presented in both tabular and 3D graphs, for ease of comparison.