Simulating time evolution with bvp4c

Dear all,

is there any way to simulate the time evolution of a BVP with bvp4c? I have a problem with a moving boundary and I created a cycle over the position in time of the moving boundary. At each iteration, the bvp4c Matlab solver calculates the solution by taking as initial guess, the solution from the previous one, knowing the current position of the boundary in object. This is my trick to include time in your system of equations. But, as I am including the time evolution of temperature, I am doubting this is the right approach. I cannot use PDEs for this problem. Thank you very much.

[Torsten]

This is a PDE, so you must use them for this problem.