Implicit and Semi-implicit Numerical Schemes for the Gradient Flow of the Formation of Biological Transport Networks
Implicit and Semi-implicit Numerical Schemes for the Gradient Flow of the Formation of Biological Transport Networks
Implicit and semi-implicit time discretizations are developed for the Cai–Hu model describing the formation of biological transport networks. The model couples a nonlinear elliptic equation for the pressure with a nonlinear reaction-diffusion equation for the network conductance vector. Numerical challenges include the nonlinearity and the stiffness, thus an explicit discretization …