A numerical solution of time-fractional coupled Korteweg-de Vries equation by using spectral collection method

Abstract

In this paper, we present a numerical method proficient for solving a system of time–fractional partial differential equations. For this sake, we use spectral collection method based on shifted Chebyshev polynomials in space and finite difference method for time fractional derivative. Furthermore, we employ this method to solve the time-fractional coupled Korteweg–de Vries (KdV) equations with appropriate initial and boundary conditions. Keywords: Fractional coupled Korteweg-de Vries equation, Finite difference schemes, Chebyshev polynomials, Spectral method