Hi, jackmell,
After many trials I also realize that it is not quite possible to simply use NDSolve to get it done. Thanks for the suggestion to go to a canonicalized form and I find that one can put the e^ factor into the variables to make a better looking form. I find that I made a...
I have a pde set as following:
parameters: γ, ω, α, β, c, η
variables: z,t; x,y
want: S = S(z,t;x,y)
A = A(z,t)
∂S/∂t = -γ*S - i ω*A*exp{-i*[(-θ-α*t)*x+β*t*y]}
[∂/∂t + (1/c)*∂/∂t] A = -i η*∫∫dxdy S*exp{i*[(-θ-α*t)*x+β*t*y]}
The integral range is angle:(0,2Pi), radius: (0,R)
How to...
Simon: Thank you very much! It is good to know at least in principle it works in this way, though the solution is not good at all. And how do you know the instability happens at t-->T?
jackmell： Thanks for telling me. Well, I tried to paste but it looked ugly. I'll try more. And the first PDE indeed works, though it has only three boundary/initial conditions. I'll show later.
FunkyDwarf: The initial condition is not just A number, it should be a function. But the analytical form of the function is unknown, because it is the solution of another PDE. See my example above.
The questions arises because I want to use the solution of one PDE as initial condition to solve another. Then using NDSolve, the first solution is given by InterpolatingFunction. I tried, it takes the whole afternoon, almost kills my computer but still not giving any result. Another computer...
Jack: Thanks a lot for the suggestions! About the boundary conditions, I find that if I eliminate S[z, 0] == 0 then Mathematica will work. If I add it, and in addition do as Hepth suggested, it also works. Now in your reply, 6 conditions are specified. Is there any way to justify Mathematica's...
Bill: Those Method options are not available somehow. It is strange--the second link you provided says explicitly that "The differential equations in NDSolve can involve complex numbers. "
BTW, the above is the complete code. No additional functions are used. Although it is not the original...