Is it possible to solve the mixed PDEs below using the method of lines or any other numerical scheme?
theta(0,t) = theta(d,t) = 0
v(0,t) = v(d,t) = 0
I.C: theta(z,0) = \thetab*sin(pi/2)*z, v(z,0) =0 at t =0 for both the initial conditions, where thetab = 0.0001
K3 = 7.5*10^(-12);
eta2 = 0.1361;
alpha2 = -0.1104;
gamma1 = 0.1093;
d = 0.0002;
xi = 0.1;
Note: xi is the controlling parameter. For instance, we can plot theta and v for different values of xi.
I tried matlab but no standard scheme to solve the problem because of the partial^2 theta/partial d partial t term. It would have been possible to use pdepe in Matlab if not for the mixed derivative. Please any help.