I have a similar system of nonlinear PDEs where I have an extra time-derivative in one equation (the same as eqautin (1c) in the attached file for the original question nonlinear_wake.pdf). Can "pdepe" solve these system of equations? If yes, how? (because I did not see it in the definition of pdepe in matlab) and if not which other method do you suggest?
Thank you very much.