The discussion focuses on solving the integral equation f(s) = ∫01 (1 + st) / (1 - st)3 f(t) dt, which features a singularity at the endpoint 1. Participants suggest that numerical algorithms, particularly those based on quadrature rules, can effectively handle such singularities. The Nystrom method is mentioned as a potential approach, though its applicability to this specific integral equation is questioned. Overall, the conversation emphasizes the need for selecting appropriate numerical methods for singular kernels.
PREREQUISITESMathematicians, numerical analysts, and researchers working on integral equations with singularities, particularly those interested in numerical methods like the Nystrom method.
Which numerical algorithm are you using? Most will quite happily handle end-point singularities.rplcs said:I am trying to solve this integral equation numerically. The kernel has a singularity at the endpoint 1. Any suggestions??
f(s) = \int_0^1 \frac{1+st}{(1-st)^3} f(t) dt
Hootenanny said:Which numerical algorithm are you using? Most will quite happily handle end-point singularities.