A boundary preserving numerical scheme for the Wright-Fisher model

Ioannis S. Stamatiou

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arXiv · 1704.04227

A boundary preserving numerical scheme for the Wright-Fisher model

Ioannis S. Stamatiou

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Abstract

We are interested in the numerical approximation of non-linear stochastic differential equations (SDEs) with solution in a certain domain. Our goal is to construct explicit numerical schemes that preserve that structure. We generalize the semi-discrete method \emph{Halidias N. and Stamatiou I.S. (2016), On the numerical solution of some non-linear stochastic differential equations using the Semi-Discrete method, Computational Methods in Applied Mathematics,16(1)} and propose a numerical scheme, for which we prove a strong convergence result, to a class of SDEs that appears in population dynamics and ion channel dynamics within cardiac and neuronal cells. We furthermore extend our scheme to a multidimensional case.

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Ioannis S. Stamatiou. 2017-04-13. A boundary preserving numerical scheme for the Wright-Fisher model. https://arxiv.org/abs/1704.04227

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