Is it possible to solve a non-linear elliptic PDE using pdepe? In my equation i have the elliptic terms d2u/dt2 and d2u/dx2, and also du/dt.
Thanks in advance.
Best Answer
Most likely you will need to introduce an auxiliary variable, v and equation du/dt = v since pdepe does not handle d2u/dt2 terms directly. So the answer is yes but it still depends on the particular form of your pde
PDEPE was designed specifically to solve first and second order parabolic-elliptic PDE's. It is possible that PDEPE may solve your higher order system after it has been transformed to multiple lower order equations. However, it may not be possible to determine ahead of time if it will be able to solve your system.
In general PDEPE does not support solving higher order equations although it may work in some cases.
I'm afraid matlab may not be able to solve coupled(interlinked) PDEs with its own pdepe function. I used that one before. However, you could always do it yourself if you could apply some numercial methods and encode yourself with soooo powerful matlab. I'd like to recommend you a software call COMSOL. It was a matlab pde toolblx and later seperated from matlab and it is dedigned to solve coupled PDEs.
Best Answer