Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

A starting method for solving nonlinear Volterra integral equations


Author: J. T. Day
Journal: Math. Comp. 21 (1967), 179-188
MSC: Primary 65.75
DOI: https://doi.org/10.1090/S0025-5718-1967-0223119-6
MathSciNet review: 0223119
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper a fifth order starting method is given for Volterra equations of the form $ y(t) = f(t) + \int_{{x_0}}^t {k(t,s,y(s))} ds$. Computational examples are given for the method as a starting method for the Gregory-Newton method.


References [Enhancements On Off] (What's this?)

  • [1] J. C. Burkill, The Theory of Ordinary Differential Equations, Oliver and Boyd, New York, 1962, pp. 11, 109.
  • [2] L. Fox and E. T. Goodwin, The numerical solution of non-singular linear integral equations, Philos. Trans. Roy. Soc. London. Ser. A. 245 (1953), 501–534. MR 0054355, https://doi.org/10.1098/rsta.1953.0005
  • [3] F. B. Hildebrand, Introduction to numerical analysis, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1956. MR 0075670
  • [4] J. G. Jones, On the numerical solution of convolution integral equations and systems of such equations, Math. Comp. 15 (1961), 131–142. MR 0122001, https://doi.org/10.1090/S0025-5718-1961-0122001-7
  • [5] J. Kuntzmann, ``Neuere Entwicklungen der Methode von Runge und Kutta,'' Z. Angew. Math. Mech., v. 41, 1961, pp. 28-31.
  • [6] M. Laudet & H. Oules, ``Sur l'intégration numérique deséquations intégrales du type Volterra,'' Symposium on the Numerical Treatment of Ordinary Differential Equations, Integral and Integro-differential Equations, pp. 117-121, Birkhäuser Verlag, Basel, 1960. MR 23 #B597.
  • [7] William Edmund Milne, Numerical Calculus. Approximations, Interpolation, Finite Differences, Numerical Integration, and Curve Fitting, Princeton University Press, Princeton, New Jersey, 1949. MR 0028671
  • [8] B. Noble, The numerical solution of nonlinear integral equations and related topics, Nonlinear Integral Equations (Proc. Advanced Seminar Conducted by Math. Research Center, U.S. Army, Univ. Wisconsin, Madison, Wis., 1963) Univ. Wisconsin Press, Madison, Wis., 1964, pp. 215–318. MR 0173369
  • [9] B. Noble, Numerical Methods, Vol. 2: Differences, Integration and Differential Equations, Oliver and Boyd, New York, 1964, pp. 267, 330.
  • [10] P. Pouzet, ``Mèthode d'intégration numérique deséquations intégrales et intégrodifférentielles du type de Volterra de seconde espèce. Formules de Runge Kutta,'' Symposium on the Numerical Treatment of Ordinary Differential Equations, Integral and Integro-differential Equations, pp. 362-368, Birkhäuser Verlag, Basel, 1960. MR 23 #B601.
  • [11] John Todd, Classical numerical analysis, Survey of numerical analysis, McGraw-Hill, New York, 1962, pp. 27–118. MR 0138184

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65.75

Retrieve articles in all journals with MSC: 65.75


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1967-0223119-6
Article copyright: © Copyright 1967 American Mathematical Society

American Mathematical Society