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JuliaApproximation / SingularIntegralEquations.jl

Julia package for solving singular integral equations
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SingularIntegral(::Circle,2) #45

Open MikaelSlevinsky opened 8 years ago

MikaelSlevinsky commented 8 years ago

i.e. the hypersingular integral is missing. Normal derivatives on the Circle are outward - this should help. We should be able to plug in the normal derivatives of the Helmholtz fundamental solution (in HelmholtzNeumann.jl) as they seem to be coordinate independent.

dlfivefifty commented 7 years ago

@MikaelSlevinsky I think the current implementation of Hilbert(Circle(),2) is wrong, as it should be equivalent to Derivative()*Hilbert(Circle()). Any objections to

Hilbert{DD<:Circle}(S::Laurent{DD},k) = k==1  ? ConcreteHilbert(S) : HilbertWrapper(Derivative(k-1)*Hilbert(S),k)

Then we can do SingularIntegral by multiplying by z to transform ds into dz:

function SingularIntegral{DD<:Circle}(d::Laurent{DD},k) 
    k==1  && ConcreteSingularIntegral(d) 
   z = Fun(d)
   SingularIntegralWrapper(Hilbert(d,k)[z],k)
end
MikaelSlevinsky commented 7 years ago

Yep, I think you're right. Related issue, #61.