Skip to Main Content

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.

 

Quadrature rule methods for Volterra integral equations of the first kind
HTML articles powered by AMS MathViewer

by Charles J. Gladwin PDF
Math. Comp. 33 (1979), 705-716 Request permission

Abstract:

A new class of quadrature rule methods for solving nonsingular Volterra integral equations of the first kind are introduced; these methods are based on an appropriate modification of the higher-order Newton-Gregory methods which are known to be divergent. Methods up to order six are constructed explicitly and illustrated with numerical examples.
References
  • H. Brunner, The solution of Volterra integral equations of the first kind by piecewise polynomials, J. Inst. Math. Appl. 12 (1973), 295–302. MR 329290
  • W. A. Coppel, Stability and asymptotic behavior of differential equations, D. C. Heath and Company, Boston, Mass., 1965. MR 0190463
  • R. J. Duffin, Algorithms for classical stability problems, SIAM Rev. 11 (1969), 196–213. MR 249740, DOI 10.1137/1011034
    • R. A. FUCHS & V. I. LEVIN, Functions of a Complex Variable and Some of Their Applications, Vol. II, Pergamon Press, Oxford, 1961.
  • C. J. Gladwin and R. Jeltsch, Stability of quadrature rule methods for first kind Volterra integral equations, Nordisk Tidskr. Informationsbehandling (BIT) 14 (1974), 144–151. MR 502108, DOI 10.1007/bf01932943
    • C. J. GLADWIN, Numerical Solution of Volterra Integral Equations of the First Kind, Ph.D. thesis, Dalhousie University, 1975.
  • Peter Henrici, Discrete variable methods in ordinary differential equations, John Wiley & Sons, Inc., New York-London, 1962. MR 0135729
  • Eugene Isaacson and Herbert Bishop Keller, Analysis of numerical methods, John Wiley & Sons, Inc., New York-London-Sydney, 1966. MR 0201039
  • Mituo Kobayasi, On numerical solution of the Volterra integral equations of the first kind by trapeziodal rule, Rep. Statist. Appl. Res. Un. Japan. Sci. Engrs. 14 (1967), no. 2, 1–14. MR 260221
  • John J. H. Miller, On the location of zeros of certain classes of polynomials with applications to numerical analysis, J. Inst. Math. Appl. 8 (1971), 397–406. MR 300435
  • W. Pogorzelski, Integral equations and their applications. Vol. I, International Series of Monographs in Pure and Applied Mathematics, Vol. 88, Pergamon Press, Oxford-New York-Frankfurt; PWN—Polish Scientific Publishers, Warsaw, 1966. Translated from the Polish by Jacques J. Schorr-Con, A. Kacner and Z. Olesiak. MR 0201934
  • Anthony Ralston, A first course in numerical analysis, McGraw-Hill Book Co., New York-Toronto-London, 1965. MR 0191070
    • R. WEISS, Numerical Procedures for Volterra Integral Equations, Ph.D. thesis, The Australian National University, Canberra, 1972.
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC: 65R20, 65D32
  • Retrieve articles in all journals with MSC: 65R20, 65D32
Additional Information
  • © Copyright 1979 American Mathematical Society
  • Journal: Math. Comp. 33 (1979), 705-716
  • MSC: Primary 65R20; Secondary 65D32
  • DOI: https://doi.org/10.1090/S0025-5718-1979-0521284-2
  • MathSciNet review: 521284