Communicated by M. KiraneIn this paper, we present a novel numerical scheme to solve a 1D, one-phase extended Stefan problem with fractional Caputo derivative with respect to time. The proposed method is based on a suitable choice of the new space coordinate for the subdiffusion equation and extends the front-fixing method to the subdiffusion case. In the final part, examples of numerical results are discussed.
Abstract. In this paper we present a numerical method to solve a one-dimensional, one-phase extended Stefan problem with fractional time derivative described in the Caputo sense. The proposed method is based on applying a similarity variable for the anomalous-diffusion equation and the finite difference method. In the final part, examples of numerical results are discussed.
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