Abstract
A bound is given for the error incurred by using Gregory's integration formula for solving nonlinear Volterra equations of the second kind.
Similar content being viewed by others
References
J. T. Day,On the numerical solution of linear Volterra integral equations, BIT 7 (1967), 71–72.
J. T. Day,A starting method for solving nonlinear Volterra integral equations, Mathematics of Computation 21 (1967), 179–188.
J. T. Day,Numerical solution of the convolution integral equation, BIT 9 (1969), 81–82.
L. Fox and E. T. Goodwin,The numerical solution of non-singular linear integral equations, Phil. Trans. Roy. Soc. of London, Series A Vol. 245 (1953), 501–534.
P. Henrici,Elements of Numerical Analysis, Wiley (1964).
D. F. Mayers, Private communication (1970).
B. Noble,The numerical solution of nonlinear integral equations and related topics, in Nonlinear Integral Equations, pp. 215–318, Univ. of Wisconsin Press (1964).
J. C. O'Neill and G. Byrne,A starting method for the numerical solution of Volterra's integral equation of the second kind, BIT 8 (1968), 43–47.
P. Pouzet, Méthode d'intégration numérique des equations intégrales et intégro-différentielles du type Volterra de seconde espèce, formules de Runge-Kutta, in Sumposium on the Numerical Treatment of Integral and Integro-differential Equations, pp. 362–368, Birkhäuser, Basel (1960).
J. Todd,A Survey of Numerical Analysis, pp. 72–73, McGraw-Hill (1962).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Phillips, G.M. An error estimate for Volterra integral equations. BIT 11, 181–186 (1971). https://doi.org/10.1007/BF01934366
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01934366