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Question: Numerical schemes for second order mixed PDEs in maple

Question:Numerical schemes for second order mixed PDEs in maple

ijuptilk 100 Maple
pde numeric differential-equations
July 28 2022
0

Is it possible to solve the mixed PDEs below using the method of lines or any other numerical scheme?

B.C:

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 

% parameters.

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.

Thank you
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