Numerical complete solution for random genetic drift by energetic variational approach

Chenghua Duan, Chun Liu, Cheng Wang, Xingye Yue

Research output: Contribution to journalArticlepeer-review

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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 languageEnglish (US)
Pages (from-to)615-634
Number of pages20
JournalESAIM: Mathematical Modelling and Numerical Analysis
Volume53
Issue number2
DOIs
StatePublished - 2019

All Science Journal Classification (ASJC) codes

  • Analysis
  • Numerical Analysis
  • Modeling and Simulation
  • Computational Mathematics
  • Applied Mathematics

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