Skip to main content
Log in

On one polynomial method of solving integral equations of the third kind

  • Published:
Russian Mathematics Aims and scope Submit manuscript

Abstract

We propose and substantiate a special variant of the subdomain-collocation method for the approximate solving integral equations of the third kind in the general case of zeros of the coefficient in the space of distributions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Bart, G. R., Warnock, R. L. “Linear Integral Equations of the Third-Kind,” SIAM J. Math. Anal. 4, No. 4, 609–622 (1973).

    Article  MathSciNet  MATH  Google Scholar 

  2. Case, K.M., Zweifel, P. F. Linear Transport Theory (Addison-Wesley, Reading, Mass., 1967; Mir, Moscow, 1972).

    MATH  Google Scholar 

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

    Google Scholar 

  4. Gabbasov, N. S., Solov’eva, S. A. “On the Theory of Solvability of Integral Equations of the Third Kind,” in Proceedings of All-Russia Scientific Conference ‘Mathematical Modeling and Boundary-Value Problems’. Part 3: ‘Differential Equations and Boundary-Value Problems’, Samara, May 29–31, 2005 (Samara, 2005), pp. 68–72 [in Russian].

    Google Scholar 

  5. Solov’eva, S. A. “Generalized Subdomain Method for a Class of the Third Kind Integral Equations,” in Proceedings of 3rd All-Russia Scientific Conference ‘Mathematical Modeling and Boundary-Value Problems’. Part 3: ‘Mathematical Differential Equations and Boundary-Value Problems’, Samara, May 29–31, 2006 (Samara, 2006), pp. 209–212 [in Russian].

    Google Scholar 

  6. Gabbasov, N. S., Solov’eva, S. A. “Generalized Moment Method for a Class of Integral Equations of the Third Kind,” Differential Equations 42, No. 10, 1490–1498 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  7. Gabbasov, N. S. Solov’eva, S. A. “A Spline Method for the Solution of Integral Equations of the Third Kind,” Russian Mathematics (Iz. VUZ) 51, No. 3, 1–8 (2007).

    MathSciNet  MATH  Google Scholar 

  8. Gabbasov, N. S., Solov’eva, S. A. “Special Versions of the Collocation Method for a Class of Integral Equations of the Third Kind,” Russian Mathematics (Iz. VUZ) 56, No. 8, 22–27 (2012).

    MathSciNet  MATH  Google Scholar 

  9. Solov’eva, S. A. “On Direct Methods of Solving Integral Equations of the Third Kind in the Space of Generalized Functions,” Candidate’s Dissertation in Mathematics and Physics (Kazan. Univ., Kazan, 2007) [in Russian].

    Google Scholar 

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

    Google Scholar 

  11. Prößorf S. “Über Systeme von singulären Integralgleichungen mit einem verschwindenden Symbol,” Mat. Issled. 7, No. 2(24), 129–142 (1972) [in Russian].

    MathSciNet  Google Scholar 

  12. Natanson, I. P. Constructive Function Theory (Gostekhizdat, Moscow, Leningrad, 1949) [in Russian].

    Google Scholar 

  13. Edwards R. Functional Analysis: Theory and Applications (Holt, Rinehart and Winston, New York, 1965; Moscow, Mir, Moscow, 1971).

    MATH  Google Scholar 

  14. Daugavet, I. K. Introduction to the Theory of Approximation of Functions (Leningrad Univ. Press, Leningrad, 1977) [in Russian].

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to S. A. Solov’eva.

Additional information

Original Russian Text © S.A. Solov’eva, 2015, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, No. 9, pp. 46–55.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Solov’eva, S.A. On one polynomial method of solving integral equations of the third kind. Russ Math. 59, 38–46 (2015). https://doi.org/10.3103/S1066369X15090054

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1066369X15090054

Keywords

Navigation