Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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

 
 

 

An algorithm for the construction of optimal methods for the numerical solution of Volterra integral equations of the first kind


Author: C. J. Gladwin
Journal: Math. Comp. 48 (1987), 625-632
MSC: Primary 65R20; Secondary 45D05
DOI: https://doi.org/10.1090/S0025-5718-1987-0878695-X
MathSciNet review: 878695
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Optimal methods for the numerical solution of Volterra integral equations of the first kind are outlined in [3] and [4]. An explicit algorithm for the construction of such methods as well as tables of coefficients for methods with order less than or equal to eight are displayed here.


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

  • [1] R. J. Duffin, "Algorithms for classical stablity problems," SIAM Rev., v. 11, 1969, pp. 196-213. MR 0249740 (40:2981)
  • [2] P. Henrici, Discrete Variable Methods in Ordinary Differential Equations, Wiley, New York, 1962. MR 0135729 (24:B1772)
  • [3] C. J. Gladwin, "On optimal integration methods for Volterra integral equations of the first kind," Math. Comp., v. 39, 1982, pp. 511-518. MR 669643 (83k:65099)
  • [4] C. J. Gladwin, "Quadrature rule methods for Volterra integral equations of the first kind," Math. Comp., v. 33, 1979, pp. 705-716. MR 521284 (80f:65144)
  • [5] C. J. Gladwin, Numerical Solution of Volterra Integral Equations of the First Kind, Ph. D. Thesis, Dalhousie University, Halifax, N. S., 1975.
  • [6] 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)
  • [7] M. Marden, Geometry of Polynomials, 2nd ed., Math. Surveys, No. 3, Amer. Math. Soc., Providence, R. I., 1966. MR 0225972 (37:1562)
  • [8] A. Ralston, A First Course in Numerical Analysis, MacGraw-Hill, New York, 1965.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65R20, 45D05

Retrieve articles in all journals with MSC: 65R20, 45D05


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1987-0878695-X
Keywords: Quadrature rule methods, Volterra integral equations of the first kind, numerical stability
Article copyright: © Copyright 1987 American Mathematical Society

American Mathematical Society