A boundary preserving numerical scheme for the Wright-Fisher model
For researchers in computational mathematics and biophysics, this provides a structure-preserving numerical method for SDEs with domain constraints, though it is an incremental extension of existing semi-discrete techniques.
The paper develops an explicit numerical scheme for non-linear stochastic differential equations (SDEs) that preserves the solution within a given domain, proving strong convergence. The method is applied to population dynamics and ion channel models, with extension to multidimensional cases.
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.