High-Order Approximation to Caputo Derivatives and Caputo-type Advection–Diffusion Equations: Revisited. (3rd July 2017) - Li, Changpin; Cai, Min
ABSTRACT: In this paper, a series of new high-order numerical approximations to α -th Caputo derivatives (0< α <2) is derived based on a compound of shift operators and high-order approximations to Riemann–Liouville derivatives. The convergence order is independent of the derivative order α, rather than the previous error estimates. Several numerical examples including the Caputo-type advection–diffusion equation are displayed, which support the derived numerical schemes.