Abstract
The Volterra integral equation of the second kind is approximated by rational predictor-corrector formulas, derived through osculatory rational interpolation. A fourth order method is treated explicitly. Convergence and A-stability are considered. For some nonlinear and singular equations, numerical results are included, and compared with results from a analougous linear method.
Keywords
- Volterra Integral Equation
- Rational Algorithm
- Rational Interpolation
- Singular Equation
- Fourth Order Method
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
F.G. TRICOMI: Integral equations, Interscience, New York (1957).
C.T.H. BAKER: The numerical treatment of integral equations, Oxford (1977).
P. POUZET: Etude en vue de leur traitement numérique des équations intégrales de type Volterra. Rev. Franç. Trait. de l'inform. (1963), pp. 79–112.
L. GAREY: Predictor-corrector methods for nonlinear Volterra integral equations of the second kind, BIT 12 (1972), pp. 325–333
J.D. LAMBERT and B. SHAW: On the numerical solution of y′ = f(x,y) by a class of formulae based on rational approximation. Mathematics of Computation 19 (1965), pp. 456–462.
H.C. THACHER, Jr.: Closed rational integration formulas. The Computer Journal, Vol.8, (1966) pp. 362–367.
Y.L. LUKE, W. FAIR, J. WIMP: Predictor-corrector formulas based on rational interpolants. Computers & Maths. with Applic., Vol 1, (1975), pp. 3–12.
P. POUZET: Algorithme de résolution des équations intégrales de type Volterra par des méthodes parpas. Rev. Franç. Trait. de l'inform. (1964), pp. 169–173.
T. SATO: Sur l'équation intégrale non linéaire de Volterra. Compositio Mathematica 11 (1953), pp. 271–290.
V.I. SMIRNOV: A course of higher mathematics, part I. Elementary Calculus, Pergamon Press 1964.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1979 Springer-Verlag
About this paper
Cite this paper
Clarysse, T.H. (1979). Rational predictor-corrector methods for nonlinear volterra integral equations of the second kind. In: Wuytack, L. (eds) Padé Approximation and its Applications. Lecture Notes in Mathematics, vol 765. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0085586
Download citation
DOI: https://doi.org/10.1007/BFb0085586
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-09717-4
Online ISBN: 978-3-540-38511-0
eBook Packages: Springer Book Archive
