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Write a complex PDE with proper format for NDSolve?

Posted 6 months ago
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Hello, I would like to write the given PDE for NDSolve,

enter image description here

with the given initial conditions:

psi(r,0)=1 psi(0,phi)=0

psi'(r,0)=0 psi'(0,phi)=0

psi''(r,0)=10 psi''(0,phi)=10

How do I write that in NDSolve form?

I tried the following test:

uval =  NDSolveValue[{i*r^3*D[u[r,y],r,r,r]+r^2*D[Tan[y]*u[r,y],r,r]+r*D[Tan[y],r]*r*i*D[u[r,y],r]+r*i*D[(Tan[y])^2*u[r,y],r]+Tan[y]*r*i*D[u[r,y],r]+Tan[y]*r*i*D[Tan[y]*u[r,y],r]+(Tan[y])^2*r*i*D[u[r,y],r]+(Tan[y])^3*i*u[r,y]==2*u[r,y]*r^2/(Cos[y])^5, u[r, -3] == u[r, 3] == u[-3, y] == u[3, y] == 0}, u, {r, -3, 3}, {y, -3, 3}]

However it says:

"NDSolveValue::femcmsd: The spatial derivative order of the PDE may not exceed two."


Posted 6 months ago
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