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Interpolation of function

My notebook is located here

My problem is that the interpolating function looks nothing like the
true function for some specific parameter values (u,r,lambda). I
changed the number of points at which the evaluation is performed but
it did not help.

My original problem is that I would like to find a crude approximation
to the original function for some parameters (u,r,lambda), where
u>1,r>1 and 0<lambda<u/(1+u). If it is not possible to do it for
general parameters then some grid with different variables' values is
fine too.

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