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The method of mechanical quadratures for integral equations with fixed singularity

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Abstract

We investigate the method of mechanical quadratures for integral equations with fixed singularity. We establish estimates of the error of this method based on a quadrature process, which is the best in the class of differentiable functions. We prove the convergence of the method in finite-dimensional and uniform metrics. We find that the investigated quadrature method is optimal by order on the Hölder class of functions.

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References

  1. Kantorovich, L. V., Akilov, G. P. Functional Analysis (Nauka, Moscow, 1977) [in Russian].

    MATH  Google Scholar 

  2. Kantorovich, L. V., Krylov, V. I. Approximate Methods of Higher Analysis (Fizmatgiz, Moscow, 1962) [in Russian].

    MATH  Google Scholar 

  3. Gavurin M.K. Lectures on Methods of Computations (Nauka, Moscow, 1971) [in Russian].

    MATH  Google Scholar 

  4. Gabdulkhaev, B. G. Optimal Approximations of Solutions to Linear Problems (Kazan Univ. Press, Kazan, 1980) [in Russian].

    MATH  Google Scholar 

  5. Lifanov, I. K. Method of Singular Integral Equations and Numerical Experiment (TOO “Yanus”, Moscow, 1995) [in Russian].

    MATH  Google Scholar 

  6. Gabbasov, N. S. “An Optimal Method for Third-Kind Integral Equations”, Dokl.Math. 58, No. 2, 177–179 (1998).

    MATH  Google Scholar 

  7. Gabbasov, N. S. “Methods for Solving Linear Integral Equation with Kernel Possessing Fixed Singularities”, Russian Mathematics (Iz. VUZ) 45, No.5, 10–18 (2001).

    MathSciNet  Google Scholar 

  8. Gabbasov, N. S. Methods for Solving Fredholm Integral Equations in Spaces of Generalized Functions (Kazan Univ. Press, Kazan, 2006) [in Russian].

    Google Scholar 

  9. Gabbasov, N. S., Zamaliev, R. R. “A Special Variant of the Subdomain Method for Integral Equations of the Third Kind with Singularities in the Kernel”, RussianMathematics (Iz. VUZ) 58, No. 10, 15–21 (2014).

    MathSciNet  MATH  Google Scholar 

  10. Onegov, L. A. “On a BestQuadrature Formula for Singular Integrals with an Immovable Singularity”, Soviet Mathematics (Iz. VUZ) 25, No. 9, 98–102 (1981).

    MathSciNet  MATH  Google Scholar 

  11. Boikov, I. V. Optimal in Exactness Algorithms for Approximate Calculation of Singular Integrasls (Saratov Univ., Saratov, 1983).

    Google Scholar 

  12. Zav’yalov, Yu. S., Kvasov, B. I., Miroshnichenko, V. L. Methods of Spline-Functions (Nauka, Moscow, 1980) [in Russian].

    MATH  Google Scholar 

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Authors and Affiliations

  1. Kazan State University of Architecture and Civil Engineering, ul. Zelyonaya 1, Kazan, 420043, Russia

    L. A. Onegov

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  1. L. A. Onegov
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Correspondence to L. A. Onegov.

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Original Russian Text © L.A. Onegov, 2016, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2016, No. 7, pp. 83–91.

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Onegov, L.A. The method of mechanical quadratures for integral equations with fixed singularity. Russ Math. 60, 71–78 (2016). https://doi.org/10.3103/S1066369X16070094

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  • DOI: https://doi.org/10.3103/S1066369X16070094

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