A boundary preserving numerical scheme for the Wright-Fisher model
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.
Keywords
Cite
@article{arxiv.1704.04227,
title = {A boundary preserving numerical scheme for the Wright-Fisher model},
author = {Ioannis S. Stamatiou},
journal= {arXiv preprint arXiv:1704.04227},
year = {2017}
}
Comments
25 pages, 4 figures. arXiv admin note: text overlap with arXiv:1309.3189