Explicit Chebyshev–Galerkin scheme for the time-fractional diffusion equation

Abstract

The time-fractional diffusion equation is applied to a wide range of practical applications. We suggest using a potent spectral approach to solve this equation. These techniques’ main objective is to efficiently solve the linear time-fractional problem by transforming it into a system of linear algebraic equations in the expansion coefficients, together with the problem’s initial and boundary conditions. The main advantage of our technique is that the resulting linear systems have special structures which facilitate their computational solution. The numerical methods are supported by a thorough convergence study for the suggested Chebyshev expansion. Some test problems are offered to demonstrate the suggested methods’ broad applicability and a high degree of accuracy.