I am looking for a numerical scheme which can easily handle the following eigen value problem

I already had the analytical results of this problem, now I want to know how to treat this problem numerically.
Any idea, then please let me know.
Thanks
I am looking for a numerical scheme which can easily handle the following eigen value problem

I already had the analytical results of this problem, now I want to know how to treat this problem numerically.
Any idea, then please let me know.
Thanks