Abstract
In this paper, we focus on numerical solutions for random genetic drift problem, which is governed by a degenerated convection-dominated parabolic equation. Due to the fixation phenomenon of genes, Dirac delta singularities will develop at boundary points as time evolves. Based on an energetic variational approach (EnVarA), a balance between the maximal dissipation principle (MDP) and least action principle (LAP), we obtain the trajectory equation. In turn, a numerical scheme is proposed using a convex splitting technique, with the unique solvability (on a convex set) and the energy decay property (in time) justified at a theoretical level. Numerical examples are presented for cases of pure drift and drift with semi-selection. The remarkable advantage of this method is its ability to catch the Dirac delta singularity close to machine precision over any equidistant grid.
Original language | English (US) |
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Pages (from-to) | 615-634 |
Number of pages | 20 |
Journal | ESAIM: Mathematical Modelling and Numerical Analysis |
Volume | 53 |
Issue number | 2 |
DOIs | |
State | Published - 2019 |
All Science Journal Classification (ASJC) codes
- Analysis
- Numerical Analysis
- Modeling and Simulation
- Computational Mathematics
- Applied Mathematics