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

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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 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.

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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