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A cubature method for solving one class of multidimensional weakly singular integral equations. (English. Russian original) Zbl 1192.65155
Russ. Math. 53, No. 12, 1-10 (2009); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2009, No. 12, 3-13 (2009).
The authors study a cubature method described by B. G. Gabdulkhaev [Izv. Vyssh. Uchebn. Zaved., Mat. 1972, No. 12 (127), 23–39 (1972; Zbl 0283.65070)] for solving one class of multidimensional weakly singular integral equations. In their investigation authors consider one class of two dimensional weakly singular integral equations of the second kind on a circumference. Authors use a special cubature formula for solving these class of multi dimensional weakly singular integral equations.

MSC:
65R20 Numerical methods for integral equations
65D32 Numerical quadrature and cubature formulas
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
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