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Quadrature rule methods for Volterra integral equations of the first kind

Author: Charles J. Gladwin
Journal: Math. Comp. 33 (1979), 705-716
MSC: Primary 65R20; Secondary 65D32
MathSciNet review: 521284
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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.

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  • [1] H. BRUNNER, "The solution of Volterra integral equations of the first kind by piecewise polynomials," J. Inst. Math. Appl., v. 12, 1973, pp. 295-302. MR 0329290 (48:7632)
  • [2] W. A. COPPEL, Stability and Asymptotic Behaviour of Differential Equations, Heath Mathematical Monographs, Boston, Mass., 1965. MR 0190463 (32:7875)
  • [3] R. J. DUFFIN, "Algorithms for classical stability problems," SIAM Rev., v. 11, 1969, pp. 196-213. MR 0249740 (40:2981)
  • [4] R. A. FUCHS & V. I. LEVIN, Functions of a Complex Variable and Some of Their Applications, Vol. II, Pergamon Press, Oxford, 1961.
  • [5] C. J. GLADWIN & R. JELTSCH, "Stability of quadrature rules for first kind Volterra integral equations," BIT, v. 14, 1974, pp. 144-151. MR 0502108 (58:19272)
  • [6] C. J. GLADWIN, Numerical Solution of Volterra Integral Equations of the First Kind, Ph.D. thesis, Dalhousie University, 1975.
  • [7] P. HENRICI, Discrete Variable Methods in Ordinary Differential Equations, Wiley, New York, 1962. MR 0135729 (24:B1772)
  • [8] E. ISAACSON & H. B. KELLER, Analysis of Numerical Methods, Wiley, New York, 1962. MR 0201039 (34:924)
  • [9] M. KOBAYASI, "On the numerical solution of the Volterra integral equation of the first kind by the trapezoidal rule," Rep. Statist. Appl. Res. Un. Japan. Sci. Engrs., v. 14, 1967, pp. 1-14. MR 0260221 (41:4849)
  • [10] J. J. H. MILLER, "On the location of zeroes of certain classes of polynomials with applications to numerical analysis," J. Inst. Math. Appl., v. 8, 1971, pp. 397-406. MR 0300435 (45:9481)
  • [11] W. POGORZELSKI, Integral Equations and Their Applications, Vol. 1, Pergamon Press, Oxford, 1966. MR 0201934 (34:1811)
  • [12] A. RALSTON, A First Course in Numerical Analysis, McGraw-Hill, New York, 1965. MR 0191070 (32:8479)
  • [13] R. WEISS, Numerical Procedures for Volterra Integral Equations, Ph.D. thesis, The Australian National University, Canberra, 1972.

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Keywords: Quadrature rule methods, Volterra integral equations of the first kind
Article copyright: © Copyright 1979 American Mathematical Society

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