Solving a set of PDEs

i need to solve a set of 5 PDEs for functions u(x,t).

i looked up the function pdepe of matlab: http://www.mathworks.com/help/matlab/math/partial-differential-equations.html?refresh=true#f1-697343

it looked perfect for my case, untill i read the line "f(x,t,u,∂u/∂x) is a flux term and s(x,t,u,∂u/∂x) is a source term. The flux term must depend on ∂u/∂x."

in my problem for 4/5 of my equations f(x,t,u,∂u/∂x) doesn't depend on ∂u/∂x, and in 1/5 of my equations f(x,t,u,∂u/∂x)=0. in my equations, theres no second derivative of u with respect to x.

does this mean i can't use pdepe in order to obtain a solution for my problem?

oddly enough, in the link for the pdepe function: http://www.mathworks.com/help/matlab/ref/pdepe.html

that line i mentioned before: "...The flux term must depend on ∂u/∂x." does not there. also, i would expect that since having f(x,t,u,∂u/∂x) that does not depend on ∂u/∂x is just a special case, it wouldn't in any way prevent me from obtaining a solution.

so all in all, i want to know if i can use pdepe even if f(x,t,u,∂u/∂x) does not depend on ∂u/∂x?

if not, what would happen if i try to solve it anyways? and what other method i can use to solve my set of PDEs?

[Po-Chien Huang]

I think the link below might help you. Because f is treated as a matrix in Matlab, you can try to set only some elements in f to depend of dudx. And of cource you can set the f to be independent of dudx,

https://www.mathworks.com/help/matlab/math/solve-system-of-pdes.html