SingularIntegralEquations.jl
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Stokes flow
This would be a good example for systems, and the fundamental solutions are known:
http://www.researchgate.net/profile/Murugesan_Krishnan2/publication/222666242_The_method_of_fundamental_solutions_for_2D_and_3D_Stokes_problems/links/0046352a8121f71bee000000.pdf