摘要：In this article, we consider the classically ill-posed problem of numerical differentiation in the framework of the PDEs-based numerical differentiation methods. A novel scheme for the first and second order numerical derivatives is proposed by the approach of an inverse source problem for a time-fractional diffusion equation. The numerical differentiation problem is transformed into the inverse source problem which induces a regularized optimization problem. The convergence rates of regularization solutions are derived under the a priori and a posteriori strategies for selecting regularization parameters, respectively. Finally, several examples are given to verify the efficiency and st ability of the proposed scheme.

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