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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A starting method for solving nonlinear Volterra integral equations
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by J. T. Day PDF
Math. Comp. 21 (1967), 179-188 Request permission

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
    J. C. Burkill, The Theory of Ordinary Differential Equations, Oliver and Boyd, New York, 1962, pp. 11, 109.
  • 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 54355, DOI 10.1098/rsta.1953.0005
  • F. B. Hildebrand, Introduction to numerical analysis, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1956. MR 0075670
  • J. G. Jones, On the numerical solution of convolution integral equations and systems of such equations, Math. Comp. 15 (1961), 131–142. MR 122001, DOI 10.1090/S0025-5718-1961-0122001-7
  • J. Kuntzmann, “Neuere Entwicklungen der Methode von Runge und Kutta,” Z. Angew. Math. Mech., v. 41, 1961, pp. 28–31. 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.
  • William Edmund Milne, Numerical Calculus. Approximations, Interpolation, Finite Differences, Numerical Integration, and Curve Fitting, Princeton University Press, Princeton, N.J., 1949. MR 0028671
  • 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
  • B. Noble, Numerical Methods, Vol. 2: Differences, Integration and Differential Equations, Oliver and Boyd, New York, 1964, pp. 267, 330. 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.
  • John Todd, Classical numerical analysis, Survey of numerical analysis, McGraw-Hill, New York, 1962, pp. 27–118. MR 0138184
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Additional Information
  • © Copyright 1967 American Mathematical Society
  • 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