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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 method for solving nonlinear Volterra integral equations of the second kind
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by Peter Linz PDF
Math. Comp. 23 (1969), 595-599 Request permission

Abstract:

The approach given in this paper leads to numerical methods for Volterra integral equations which avoid the need for special starting procedures. Formulae for a typical fourth-order method are derived and some numerical examples presented. A convergence theorem is given for the method described.
References
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  • 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
    • P. Linz, The Numerical Solution of Volterra Integral Equations by Finite Difference Methods, MRC Technical Summary Report #825, Mathematics Research Center, University of Wisconsin, Madison, Wis., 1967. D. F. Mayers, Numerical Solution of Ordinary and Partial Differential Equations, Pergamon Press, Oxford and Addison-Wesley, Reading, Mass., 1962, Chapters 13, 14. MR 26 #4488.
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    • P. Pouzet, Étude en Vue de leur Traitment Numérique d’Équations Intégrales et IntégroDifférentielles du Type de Volterra pour des Problèmes de Conditions Initiales, Thesis, University of Strassbourg, 1962. P. Pouzet, "Méthode d’intégration numérique des équations intégrales et intégro-différentielles 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, (Rome, 1960), Birkhäuser Verlag, Basel, 1960, pp. 362–368. MR 23 #B601.
  • F. G. Tricomi, Integral equations, Pure and Applied Mathematics, Vol. V, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1957. MR 0094665
  • Andrew Young, The application of approximate product integration to the numerical solution of integral equations, Proc. Roy. Soc. London Ser. A 224 (1954), 561–573. MR 63779, DOI 10.1098/rspa.1954.0180
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Additional Information
  • © Copyright 1969 American Mathematical Society
  • Journal: Math. Comp. 23 (1969), 595-599
  • MSC: Primary 65.75
  • DOI: https://doi.org/10.1090/S0025-5718-1969-0247794-7
  • MathSciNet review: 0247794