Abstract
ABSTRACTIn 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.
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