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Numerical solution of the singular Abel integral equation by the generalized quadrature method. (English. Russian original) Zbl 1100.65128
Russ. Math. 48, No. 8, 59-66 (2004); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2004, No. 8, 62-70 (2004).
From the introduction: We consider the singular integral equation of the first kind \[ \int^R_x\frac{s}{\sqrt{s^2-x^2}}y(s)ds=f(x),\quad 0\leq x\leq R, \] where \(y(s)\) is the desired function and in particular, \(R=\infty\), and with a variable lower limit (the Abel integral equation), and the generalized quadrature method for its solution.

65R20 Numerical methods for integral equations
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)