Solving PDE with imaginary unit ?

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Question:Solving PDE with imaginary unit ?

Posted: Mariusz Iwaniuk 1526 Product: Maple 2022

February 25 2023

I want solve PDE equation with imaginary unit ,but Maple give me an Error:

(1)

sol := pdsolve(I*(diff(M(r, t), t)) = -exp(-M(r, t))*(diff(M(r, t), r, r)-(diff(M(r, t), r))^2+2*(diff(M(r, t), r))/r), [M(r, 0) = (1/4)*exp(-(1/2)*r^2), (D[1](M))(eps, t) = 0, M(inf, t) = 0], numeric, time = t, range = eps .. inf, abstol = 0.1e-2)

vals := sol:-value(M(r, t), output = listprocedure)

U := eval(M(r, t), vals)

Error, (in solnproc) unable to compute solution for t>0.:
unable to propagate solution at minimum time step, decreasing 'mintimestep' and/or 'spacestep' may take care of this problem, or solution may be unstable (e.g. formation of a shock layer)

Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

Download PDE_with_Imaginary_Unit.mw

If I delete Imaginary unit from equation Maple give me a solution.

Thanks .

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Question: Solving PDE with imaginary unit ?

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