| Summary: | This article is devoted to <span style="font-variant: small-caps;">Feller</span>’s diffusion equation, which arises naturally in probability and physics (e.g., wave turbulence theory). If discretized naively, this equation may represent serious numerical difficulties since the diffusion coefficient is practically unbounded and most of its solutions are weakly divergent at the origin. In order to overcome these difficulties, we reformulate this equation using some ideas from the <span style="font-variant: small-caps;">Lagrangian</span> fluid mechanics. This allows us to obtain a numerical scheme with a rather generous stability condition. Finally, the algorithm admits an elegant implementation, and the corresponding <span style="font-variant: small-caps;">Matlab</span> code is provided with this article under an open source license.
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