The Gα -scheme for Approximation of Fractional Derivatives: Application to the Dynamics of Dissipative Systems

The Gear scheme is a three-level step algorithm, backward in time and second order accurate, for the approximation of classical time derivatives. In this article, the formal power of this scheme is used to approximate fractional derivative operators, in the context of finite difference methods. Numerical examples are presented and analyzed, in order to show the accuracy of the Gear scheme at the power α (Gα-scheme) when compared to the classical Grunwald-Letnikov approximation. In particular, the combined Gα -Newmark scheme is shown to be second-order accurate for a fractional damped oscillator problem.