cell-migration-similarity-soln

The MATLAB code contained in the cell-migration-similarity-soln project was developed for the work described in:

Tracy L. Stepien and Hal L. Smith, Existence and uniqueness of similarity solutions of a generalized heat equation arising in a model of cell migration, Discrete Contin. Dyn. Syst., 35 (2015), 3203-3216, DOI: 10.3934/dcds.2015.35.3203.

Numerical solutions of the boundary value problem (Equation 20)

where c, n, and a are parameters, are obtained by using a shooting method combined with the secant method.

Programs

• program_solve_bvp.m: run this program to solve the boundary value problem
• program_buildstablemanifold.m: run this program to solve many boundary value problems and save the corresponding x(0) and x'(0) values in a .mat file
• program_solve_ivp.m: run this program to solve the initial value problem (no boundary condition at t->infinity)

Plots

• plot_of_sims.m - reproduce Figure 1

• plot_of_manifold.m - reproduce Figure 3

Auxiliary Files

• secant.m
• selfsimJac.m
• selfsimODE.m
• shoot.m
• solveBVP.m
• solveIVP.m

Data Files

• data/n0_data.mat
• data/n2_data.mat
• data/n3_data.mat
• data/n5_data.mat
• data/samplesim_n2_c25_y0_np5.mat
• data/samplesim_n2_c25_y0_p5.mat

Licensing

Copyright 2013-2015 Tracy Stepien. This is free software made available under the MIT License. For details see the LICENSE file.