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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 contribution, the formal power of this scheme is proposed to approximate fractional derivative operators in the context of finite difference methods. Some numerical examples are presented and analysed in order to show the effectiveness of the present Gear scheme at the power a (G a-scheme) when compared to the classical Gru¨nwald-Letnikov approximation. In particular, for a fractional damped oscillator problem, the combined G a-Newmark scheme is shown to be second-order accurate.

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We review the difficulties of a modal approach when modeling a Reverberation Chamber (RC) by the Finite Element Method (FEM). The numerical challenge is due to the large scale problem involved by the over-dimensioned cavity. Moreover, the field singularity on the stirrer has to be captured by the FEM. First the following issues are discussed: existence of nullfrequency solutions, convergence rate for h and p adaption, and formulation type in E or H field. Then the modal analysis is compared to the classical harmonic one. A focus is put on the field singularity at the source point.

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