Numerical simulation of Feller's diffusion 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.

22 pages, 2 tables, 4 figures, 3 appendices, 25 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/

References in corpus (4)

• On supraconvergence phenomenon for second order centered finite differences on non-uniform grids
• Non-stationary Feller process with time-varying coefficients
• Numerical simulation of conservation laws with moving grid nodes: Application to tsunami wave modelling
• Nonstationary distributions of wave intensities in Wave Turbulence