13:45 - 14:45, June 20, 2025 (Friday) Room 515, Cosmology Building, National Taiwan University + Zoom, Physical+Online Seminar
(實體+線上演講 台灣大學次震宇宙館515研討室+ Zoom)
On a Modified Random Genetic Drift Model: Derivation and a Structure-Preserving Operator-Splitting Discretization Chi-An Chen (Illinois Institute of Technology)
Abstract
The Kimura equation models random genetic drift as a diffusion process, but its degeneracy at the boundaries prevents imposing biologically meaningful boundary conditions while maintaining classical solutions. We propose a modified model by restricting the domain to and applying Robin-type boundary conditions. To capture fixation behavior, we introduce two variational parameters near the boundaries. We also develop a hybrid Eulerian-Lagrangian operator splitting scheme: a Lagrangian step handles interior dynamics with a no-flux condition, followed by an Eulerian update near the boundaries. This scheme preserves mass, positivity, and the first moment. Numerical tests confirm its efficiency and structure-preserving properties.
