Tau Approach for the Time-Fractional Diffusion Equation Using Certain Chebyshev Polynomials (European Journal of Pure and Applied Mathematics, 2025)
This research article presents a numerical technique for solving the time-fractional diffusion equation (TFDE). The approach uses Certain Chebyshev polynomials as basis functions. These polynomials are particular cases of the generalized Gegenbauer polynomials. The operational matrices of integer and fractional derivatives are used, along with the tau method, for the spatialand temporal discretization. Hence, the problem with its underlying conditions is converted into a system of equations that can be handled. We investigate the convergence of the double Chebyshev expansion and derive rigorous error bounds. Numerical examples show the method’s superior accuracy and efficiency over some existing methods in the literature.
Keywords: Time-fractional diffusion equation; Chebyshev polynomials; Tau method; convergence analysis