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A cubature method for solving one class of multidimensional weakly singular integral equations

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Abstract

In this paper we consider one class of two-dimensional weakly singular integral equations of the second kind on a circumference. We theoretically prove the applicability of a cubature method based on a special cubature formula for solving equations of the mentioned class.

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References

  1. S. G. Mikhlin, Multidimensional Singular Integrals and Integral Equations (Fizmatgiz, Moscow, 1962; Pergamon Press, Oxford, 1965).

    Google Scholar 

  2. V. Z. Parton and P. I. Perlin, Integral Equations of Elasticity Theory (Nauka, Moscow, 1977) [Russian translation].

    Google Scholar 

  3. M. V. Khai, Two-Dimensional Integral Equations in Newton Potentials and Their Applications (Naukova Dumka, Kiev, 1993) [in Russian].

    Google Scholar 

  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).

  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.

    Google Scholar 

  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).

    Google Scholar 

  8. G. Szegö, Orthogonal Polynomials (Fizmatgiz, Moscow, 1962; American Mathematical Society Colloquium Publications, Vol. 23, Providence, RI, 1978).

    MATH  Google Scholar 

  9. A. Kh. Turetskii, The Interpolation Theory in Problems (Vysshaya Shkola, Minsk, 1968) [in Russian].

    Google Scholar 

  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].

    Google Scholar 

  12. S. N. Bernshtein, Collection of Works (Akad. Nauk SSSR, Moscow, 1954) [in Russian], Vol. II.

    Google Scholar 

  13. B. G. Gabdulkhaev, “Direct Methods of Solution of Certain Operator Equations. I,” Izv. Vyssh. Uchebn. Zaved. Mat., No. 11, 33–44 (1971).

  14. B. G. Gabdulkhaev, “Direct Methods of Solution of Certain Operator Equations. II,” Izv. Vyssh. Uchebn. Zaved. Mat., No. 12, 28–38 (1971).

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Correspondence to Yu. R. Agachev.

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Original Russian Text © Yu.R. Agachev and R.K. Gubaidullina, 2009, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2009, No. 12, pp. 3–13.

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Agachev, Y.R., Gubaidullina, R.K. A cubature method for solving one class of multidimensional weakly singular integral equations. Russ Math. 53, 1–10 (2009). https://doi.org/10.3103/S1066369X09120019

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  • DOI: https://doi.org/10.3103/S1066369X09120019

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