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Question: solve ODE with boundary conditions

Question:solve ODE with boundary conditions

arashghgood 60 Maple
numeric differential-equations
February 08 2023
0

dear all
I would like to solve the following differential equation in Maple Numerically.

restart;
pde := I*10*diff(u(k, t), t) + (diff(u(k, t), t, t)) -16* u(k, t) = 0;
ics := u(k, 0) = sqrt(Pi/2)*csch(Pi/2*k), (D[2](u))(k, 0) = -(1/4)*sqrt(2)*Pi^(3/2)*csch((1/2)*Pi*k)*coth((1/2)*Pi*k)
bcs := u(0, t) = 0, u(100, t) = 0;
sol := pdsolve(pde, {ics, bcs}, numeric, range = 0 .. 1, output = listprocedure);
sol;

here the sech(x)^2 in real space and corresponding fourier transformaation is the initial condition

the Gaussian function as initial condition is also an alternative.

How can I solve it?
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