On a Legendre Tau Method for Fractional Boundary Value Problems with a Caputo Derivative

Abstract

Abstract In this paper, we revisit a Legendre-tau method for two-point boundary value problems with a Caputo fractional derivative in the leading term, and establish an L 2 error estimate for smooth solutions. Further, we apply the method to the Sturm-Liouville problem. Numerical experiments indicatethat for the source problem, it converges steadily at an algebraic rate even for nonsmooth data, and the convergence rate enhances with problem data regularity, whereas for the Sturm-Liouville problem, it always yields excellent convergence for eigenvalue approximations.