Agachev, Yu. R.; Gubaidullina, R. K. 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. Reviewer: Seenith Sivasundaram (Daytona Beach) Cited in 1 Document 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) Keywords:weighted Lebesgue space; integral equation; weakly singular integral; Gauss quadrature formula; cubature method; convergence; error estimate PDF BibTeX XML Cite \textit{Yu. R. Agachev} and \textit{R. K. Gubaidullina}, Russ. Math. 53, No. 12, 1--10 (2009; Zbl 1192.65155); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2009, No. 12, 3--13 (2009) Full Text: DOI References: [1] S. G. Mikhlin, Multidimensional Singular Integrals and Integral Equations (Fizmatgiz, Moscow, 1962; Pergamon Press, Oxford, 1965). [2] V. Z. Parton and P. I. Perlin, Integral Equations of Elasticity Theory (Nauka, Moscow, 1977) [Russian translation]. · Zbl 0394.73092 [3] M. V. Khai, Two-Dimensional Integral Equations in Newton Potentials and Their Applications (Naukova Dumka, Kiev, 1993) [in Russian]. [4] B. G. Gabdulkhaev, ”On the Integral Solution of Integral Equations by the Method of Mechanical Quadratures,” Izv. Vyssh. Uchebn. Zaved.Mat., No. 12, 23–39 (1972). · Zbl 0283.65070 [5] B. G. Gabdulkhaev and R. K. Gubaidullina, ”On Cubature Formulas for a Class of Multidimensional Weakly Singular Integrals,” in II Mizhnarodn. Naukovo-Praktichn. Konf. ’Dni Nauki-2006’. Matematika (Dnipropetrovsk, 2006), Vol. 35, pp. 12–18. [6] A. Zygmund Trigonometric Series (Cambridge University Press, 1959; Mir, Moscow, 1965), Vol. 2. [7] B. G. Gabdulkhaev, ”Cubature Formulas for Multidimensional Singular Integrals. I,” Tr. Inst. Matem. AN Bolgarii, Sofiya 11, 181–196 (1970). · Zbl 0241.65024 [8] G. Szegö, Orthogonal Polynomials (Fizmatgiz, Moscow, 1962; American Mathematical Society Colloquium Publications, Vol. 23, Providence, RI, 1978). · Zbl 0100.28405 [9] A. Kh. Turetskii, The Interpolation Theory in Problems (Vysshaya Shkola, Minsk, 1968) [in Russian]. [10] B. G. Gabdulkhaev, ”Quadrature Formulas for Singular Integrals and the Method of Mechanical Quadratures for Singular Integral Equations,” in Proceedings of International Conference on Constructive Function Theory (Varna, May 19–25, 1970), pp. 35–49. [11] V. V. Ivanov, The Theory of Approximate Methods and Its Application to the Numerical Solution of Singular Integral Equations (Naukova Dumka, Kiev, 1968) [in Russian]. [12] S. N. Bernshtein, Collection of Works (Akad. Nauk SSSR, Moscow, 1954) [in Russian], Vol. II. [13] B. G. Gabdulkhaev, ”Direct Methods of Solution of Certain Operator Equations. I,” Izv. Vyssh. Uchebn. Zaved. Mat., No. 11, 33–44 (1971). · Zbl 0277.45006 [14] B. G. Gabdulkhaev, ”Direct Methods of Solution of Certain Operator Equations. II,” Izv. Vyssh. Uchebn. Zaved. Mat., No. 12, 28–38 (1971). · Zbl 0277.45007 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.