Keywords
- Fredholm Operator
- Volterra Integral Equation
- Volterra Operator
- Chebyshev Approximation
- Volterra Type
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
P. M. Anselone, Collectively Compact Operator Approximation Theory and Application to Integral Equations, Prentice-Hall, Englewood Cliffs (N.J.), 1971.
P. M. Anselone and J. W. Lee, Double approximation schemes for integral equations, to appear in: Proc. Confer. Approximation Theory (Math. Research Inst. Oberwolfach (Germany), May 25–30, 1975), Birkhäuser-Verlag, Basel.
H. Brunner, On the approximate solution of first-kind integral equations of Volterra type, Computing (Arch. Elektron. Rechnen), 13 (1974), 67–79.
H. Brunner, Global solution of the generalized Abel integral equation by implicit interpolation, Math. Comp., 28 (1974), 61–67.
C. B. Dunham, Chebyshev approximation with a null point, Z. Angew. Math. Mech., 52 (1972), 239.
C. B. Dunham, Families satisfying the Haar condition, J. Approx. Theory, 12 (1974), 291–298.
F. R. Gantmacher und M. G. Krein, Oszillationsmatrizen, Oszillations-kerne und kleine Schwingungen mechanischer Systeme, Akademie-Verlag, Berlin, 1960.
C. J. Gladwin, Numerical Solution of Volterra Integral Equations of the First Kind, Ph.D. Thesis, Dalhousie University, Halifax, N. S., 1975.
J. Hertling, Numerical treatment of singular integral equations by interpolation methods, Numer. Math., 18 (1971/72), 101–112.
F. de Hoog and R. Weiss, On the solution of Volterra integral equations of the first kind, Numer. Math., 21 (1973), 22–32.
F. de Hoog and R. Weiss, High order methods for Volterra integral equations of the first kind, SIAM J. Numer. Anal., 10 (1973), 647–664.
P.A. Holyhead, S. McKee and P.J. Taylor, Multistep methods for solving linear Volterra integral equations of the first kind, to appear in: SIAM J. Numer. Anal.
Y. Ikebe, The Galerkin method for numerical solution of Fredholm integral equations of the second kind, SIAM Review, 14 (1972), 465–491.
J. Janikowski, Équation intégrale non linéaire d’Abel, Bull. Soc. Sci. Lettres Lódź, 13 (1962), no.11.
E.H. Kaufman and G.G. Belford, Transformation of families of approximating functions, J. Approx. Theory, 4 (1971), 363–371.
E. L. Kosarev, The numerical solution of Abel’s integral equations, Zh. vycisl. Mat. mat. Fiz., 13 (1973), 1591–1596 (=U.S.S.R. Comput. Math. and Math. Phys., 13 (1973), 271–277).
G. Kowalewski, Integralgleichungen, de Gruyter, Berlin, 1930.
P. Linz, Numerical methods for Volterra integral equations of the first kind, Comput. J., 12 (1969), 393–397.
B. Noble, The numerical solution of nonlinear integral equations and related topics, in: P.M. Anselone (Ed.), Nonlinear Integral Equations, University of Wisconsin Press, Madison, 1964: 215–318.
G. Strang and G.J. Fix, An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs (N.J.), 1973.
R. Weiss, Product integration for the generalized Abel equation, Math. Comp., 26 (1972), 177–190.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1976 Springer-Verlag
About this paper
Cite this paper
Brunner, H. (1976). The approximate solution of linear and nonlinear first-kind integral equations of Volterra type. In: Watson, G.A. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 506. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0080111
Download citation
DOI: https://doi.org/10.1007/BFb0080111
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-07610-0
Online ISBN: 978-3-540-38129-7
eBook Packages: Springer Book Archive
