Skip to main content
Log in

Solution of linear integral equations by Gregory's method

  • Published:
BIT Numerical Mathematics Aims and scope Submit manuscript

Abstract

Two techniques for using Gregory's method to solve Fredholm integral equations of the second kind are described. Since the kernel function is allowed to be mildly discontinuous, Volterra integral equations of the second kind can be solved in the same manner. Some numerical examples are given.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. P. M. Anselone,Uniform Approximation Theory for Integral Equations with Discontinuous Kernels, SIAM J. Numer. Anal.4 (1967), 245–253.

    Google Scholar 

  2. P. M. Anselone and J. M. Gonzalez-Fernandez,Uniformly Convergent Approximate Solutions of Fredholm Integral Equations, J. Math. Anal. Appl. 10 (1965), 519–536.

    Google Scholar 

  3. P. M. Anselone and R. H. Moore,Approximate Solutions of Integral and Operator Equations, J. Math. Anal. Appl. 9 (1964), 268–277.

    Google Scholar 

  4. R. J. Espinosa-Maldonado and G. D. Byrne,On the Convergence of Quadrature Formulas, SIAM J. Numer. Anal. To Appear.

  5. L. Fox and E. T. Goodwin,The Numerical Solution of Nonsingular Linear Integral Equations, Phil. Trans. A 245 (1953), 501–534.

    Google Scholar 

  6. V. I. Krylov,Application of the Euler-Laplace Formula to the Approximate Solution of Integral Equations of Volterra Type (In Russian), Trudy Mat. Inst. Steklov 28 (1949), 33–72.

    Google Scholar 

  7. D. F. Mayers,Equations of Volterra Type, Ch. 13 in Numerical Solution of Ordinary and Partial Differential Equations, L. Fox, ed. Addison-Wesley, Reading, Mass. 1962.

    Google Scholar 

  8. S. E. Mikeladze,On the Numerical Solution of Integral Equations (In Russian), Izv. Akad. Nauk. SSSR, Ser. VII (1935) No. 2, 255–300.

    Google Scholar 

  9. J. C. O'Neill,Some Numerical Solutions of Volterra's Integral Equation, Ph. D. Thesis, Univ. of Pittsburgh (1967).

  10. J. C. O'Neill and G. D. Byrne,A Starting Method for the Numerical Solution of Volterra's Integral Equation of the Second Kind, BIT 8 (1968), 43–47.

    Google Scholar 

  11. P. Pouzet, Methode d'Integration Numerique des Equations Integrales et Integegro-differentielles du Type de Volterra de Seconde Espece. Formules de Runge Kutta. In, Symposium on the Treatment of Ordinary Differential Equations, Integral and Integro-differential Equations, pp. 362–368, Birkhauser Verlag, Basel, 1960.

    Google Scholar 

  12. E. M. Sparrow,Applications of Variational Methods to Radiation Heat-Transfer Calculations, J. Heat Transfer (Nov. 1960), 377–380.

  13. F. G. Tricomi,Integral Equations, Interscience, New York, 1957.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Espinosa-Maldonado, R., Byrne, G.D. Solution of linear integral equations by Gregory's method. BIT 10, 457–464 (1970). https://doi.org/10.1007/BF01935565

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01935565

Keywords

Navigation