Numerical solution of the singular Abel integral equation by the generalized quadrature method. (English. Russian original) Zbl 1100.65128

Sizikov, V. S.; Smirnov, A. V.; Fedorov, B. A.

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)

Keywords:

singular integral equation of the first kind; Abel integral equation; generalized quadrature method