I use pdsolve to solve this system of equation but the graph I have is different from the author's graph. I think I'm missing out on something. Can anyone help me out with the solution using any Maple command and module.

PDE := {diff(phi(x, t), t) = (diff(phi(x, t), x, x))/S__c-K__r*phi(x, t)+S__r*(diff(theta(x, t), x, x)), diff(u(x, t), t) = diff(u(x, t), x, x)-M^2*(u(x, t)-m*w(x, t))/(m^2+1)-u(x, t)/`ϰ`-2*Omega^2*w(x, t)+Gr*theta(x, t)+Gm*phi(x, t), diff(w(x, t), t) = diff(w(x, t), x, x)+M^2*(m*u(x, t)-w(x, t))/(m^2+1)-w(x, t)/`ϰ`+2*Omega^2*u(x, t), diff(theta(x, t), t) = lambda*(diff(theta(x, t), x, x))/P__r}

With Inittial and boundary condition : {phi(0, t) = 1, phi(9, t) = 0, phi(x, 0) = 0, u(0, t) = t, u(9, t) = 0, u(x, 0) = 0, w(0, t) = 0, w(9, t) = 0, w(x, 0) = 0, theta(0, t) = 1, theta(9, t) = 0, theta(x, 0) = 0}

With the following parameter declared as:

I will appreciate the graph of the solution with time t:0.3, 0.5, 0.7 and 1.0.

Thanks.

How can I find the numeric value of this PDE:

Where

I want the numeric values i.e theta(2,2) , theta (1,3) and the likes.

Is Symbolic Laplace and Inverse Laplace transform possible on Maple? if Yes, how do I find the inverse laplace of this function 

Thanks.