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), 625632
MSC:
Primary 65R20; Secondary 45D05
MathSciNet review:
878695
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Abstract 
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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.
 [1]
R.
J. Duffin, Algorithms for classical stability problems, SIAM
Rev. 11 (1969), 196–213. MR 0249740
(40 #2981)
 [2]
Peter
Henrici, Discrete variable methods in ordinary differential
equations, John Wiley & Sons, Inc., New YorkLondon, 1962. MR 0135729
(24 #B1772)
 [3]
C.
J. Gladwin, On optimal integration methods for
Volterra integral equations of the first kind, Math. Comp. 39 (1982), no. 160, 511–518. MR 669643
(83k:65099), http://dx.doi.org/10.1090/S00255718198206696431
 [4]
Charles
J. Gladwin, Quadrature rule methods for Volterra
integral equations of the first kind, Math.
Comp. 33 (1979), no. 146, 705–716. MR 521284
(80f:65144), http://dx.doi.org/10.1090/S00255718197905212842
 [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 and R.
Jeltsch, Stability of quadrature rule methods for first kind
Volterra integral equations, Nordisk Tidskr. Informationsbehandling
(BIT) 14 (1974), 144–151. MR 0502108
(58 #19272)
 [7]
Morris
Marden, Geometry of polynomials, Second edition. Mathematical
Surveys, No. 3, American Mathematical Society, Providence, R.I., 1966. MR 0225972
(37 #1562)
 [8]
A. Ralston, A First Course in Numerical Analysis, MacGrawHill, New York, 1965.
 [1]
 R. J. Duffin, "Algorithms for classical stablity problems," SIAM Rev., v. 11, 1969, pp. 196213. 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. 511518. 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. 705716. 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. 144151. 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, MacGrawHill, New York, 1965.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0025571819870878695X
PII:
S 00255718(1987)0878695X
Keywords:
Quadrature rule methods,
Volterra integral equations of the first kind,
numerical stability
Article copyright:
© Copyright 1987
American Mathematical Society
