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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.

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