MATLAB code to perform numerical continuation on the Swift--Hohenberg equation: u_t = ru + (1+d_xx)^2u + nu u^2-u^3, so that solution profiles for steady state u are found as the parameter r is varied.

To run.

1. create a new directory.
2. initialise a file all_param.mat, that Contains a structure all_param, containing a structure ic with fields: r, u, nu, which correspond to the initial values of these variables/constants.
3. Within the current working directory, run contSH_main()

It is possible to specify other parameters (see examples/standard_continuation/all_param.mat and the file init_param.m for details and information about the default values.)

Notable features include:

• The ability to compute the stability of steady states (set all_param.sp.find_eval = 1)
• The ability to continue bifurcation points in (r,nu) parameter space, given initial conditions for r, nu, u and v, where v is the marginal eigenvector at the bifurcation.
• The ability to track Maxwell Points, where the free energy is 0, in (r,nu) space. (see examples/mp/)