The numerical solution of the singular integral equations has been developed by Erdogan and many other researchers (e.g., Erdogan, F., Gupta, G.D., 1972. On the numerical solution of singular integral equations. Q. Appl. Math. 29, 525–534. DOI: Article On the numerical solution of singular integral equations
), where the Gauss-Chebyshev quadrature method was proposed. However, if the kernel function of the integral is already regular, then may I ask what is the proper numerical method to deal with this issue?A necessary condition to utilize Erdogan's method is that the coefficients a_ij (please refer to the picture in the file) of the singular term are non-singular, which is not the case I would want to deal with, since those coefficients are already zero in the regular integral equations.
I would be very grateful if you can give me some guidence! Thank you very much!
Not specific but very similar work done by Prof. Abdon Atangana
e.g. you can consider following book
Numerical Methods for Fractional Differentiation
Book by Abdon Atangana and Kolade M. Owolabi
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