Behavior of different numerical schemes for random genetic drift

被引：0
作者：
Shixin Xu
Minxin Chen
Chun Liu
Ran Zhang
Xingye Yue
机构：
[1] Soochow University,School of Mathematical Sciences
[2] Illinois Institute of Technology,Department of Applied Mathematics
[3] Shanghai University of Finance and Economics,School of Mathematics
来源：
BIT Numerical Mathematics | 2019年 / 59卷
关键词：
Random genetic drift; Degenerate equation; Conservations of probability and expectation; Finite volume method; Finite difference method; Finite element method; Numerical viscosity and numerical anti-diffusion; 35K65; 65M06; 92D10;
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摘要：
In the problem of random genetic drift, the probability density of one gene is governed by a degenerated convection-dominated diffusion equation. Dirac singularities will always be developed at boundary points as time evolves, which is known as the fixation phenomenon in genetic evolution. Three finite volume methods: FVM1-3, one central difference method: FDM1 and three finite element methods: FEM1-3 are considered. These methods lead to different equilibrium states after a long time. It is shown that only schemes FVM3 and FEM3, which are the same, preserve probability, expectation and positiveness and predict the correct probability of fixation. FVM1-2 wrongly predict the probability of fixation due to their intrinsic viscosity, even though they are unconditionally stable. Contrarily, FDM1 and FEM1-2 introduce different anti-diffusion terms, which make them unstable and fail to preserve positiveness.
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页码：797 / 821
页数：24
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