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Title: Numerical complete solution for random genetic drift by energetic variational approach
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.  more » « less
Award ID(s):
1759535
PAR ID:
10095304
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
ESAIM: Mathematical Modelling and Numerical Analysis
Volume:
53
Issue:
2
ISSN:
0764-583X
Page Range / eLocation ID:
615 to 634
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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