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I was reading this paper the other day and I've been trying to find the numerical techniques its mentions but have been thus far unsuccessful. The authors simply state that is well know and straightforward, and they believe this so much that they don't even include a reference. Ok, sorry about the rant.

The general problem they are trying to solve is for the r-mode oscillations of Neutron Stars. They get everything down to a 2nd order 1-d differential equation. They say the solution is zero at r=0, and at the surface they say it obeys something like A[r] * δρ[r] + B[r] * ∂ δρ[r] / ∂r =0. They they say they integrate from r=0 with the condition that δρ [0] =0, and from the surface with the condition A[r] * δρ[r] + B[r] * ∂ δρ[r] / ∂r =0 and they match the solutions at some specified point, and they use the frequency of the mode as the parameter they mess with to match the solution.

I understand how one can integrate out to the surface with the condition that δρ [0] , but how do they does the integration from the surface to the interior work when one has a Mixed boundary condition?

Any help is greatly appreciated. Thanks.

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# Numerical Solutions for Mixed Boundary Condition

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