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Numerical solution of Feller's equation

Abstract : This article is devoted to Feller's diffusion equation which arises naturally in probabilities 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 Lagrangian 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 Matlab code is provided with this article under an open source license.
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Contributor : Denys DUTYKH Connect in order to contact the contributor
Submitted on : Tuesday, September 17, 2019 - 3:14:42 PM
Last modification on : Wednesday, November 3, 2021 - 6:17:32 AM
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Denys Dutykh. Numerical solution of Feller's equation. Mathematics , MDPI, 2019, 7 (11), pp.1067. ⟨10.3390/math7111067⟩. ⟨hal-02290284⟩



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