Fortran How to Write Fortran Code for a Complex Phase Speed

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The discussion centers on a mathematical model involving the functions hBy(y) and h0y(y) with specific parameters and conditions. The model defines maximum and minimum values of hBy(y) within a certain interval and outlines constraints on complex phase speed based on these values. The conditions for complex phase speed are categorized into three cases depending on the value of CR relative to α1 and α2. The geometric representation of the solution space is described as a rectangle with quarter circles, defined by the parameters α1, α2, µ, γ, and k. A request for assistance in writing Fortran code to implement these equations is made, but there is a reminder that a similar question has been previously asked, prompting the need for the user to show their attempts at solving the problem.
logi
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Hi,

We assume
Max hBy(y) = α1 for y ε (a1, a2) and Min hBy(y) = α2 for y ε (a1, a2)
Where -∞ < α2 ≤ α1 < ∞, and the complex phase speed must lie in the region defined by

(CR + α1 )^2 + CI^2 ≤ µγ^2/k^2, if CR <- α1

CI^2 ≤ µγ^2/k^2, if -α1≤ CR ≤-α2,

(CR + α2 )^2 + CI^2 ≤ µγ^2/k^2, if CR >- α2

Where CI ≥ 0 and γ^2= max [hBy(y) h0y(y)] >0, h0y(y)= -8(y-a)/L^2
The region represents a rectangle of length α1 - α2 with a quarter circle on each end, with the height of the rectangle and the radius of the circles given by µ^(1/2)γ/k.

Could you please help me to write the Fortran code for this equations?

Thanks
Logi
 
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