A boundary preserving numerical scheme for the Wright-Fisher model

2017/04/13 by Stamatiou, Ioannis S.
#60H10 #60H35 #65C20 #65C30 #65J15 #65L20 #92D99 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1704.04227

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 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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