## On optimal integration methods for Volterra integral equations of the first kind

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- by C. J. Gladwin PDF
- Math. Comp.
**39**(1982), 511-518 Request permission

## Abstract:

Families of methods depending on free parameters are constructed for the solution of nonsingular Volterra integral equations of the first kind in [5]. These parameters are restricted to certain regions in order that a certain polynomial satisfies both a stability and a consistency condition. In this note an optimal choice of the free parameters is outlined in order that the ${l_2}$-norm of the roots of the polynomial is minimized.## References

- Celia Andrade and S. McKee,
*On optimal high accuracy linear multistep methods for first kind Volterra integral equations*, BIT**19**(1979), no. 1, 1–11. MR**530109**, DOI 10.1007/BF01931215 - H. Brunner,
*Projection methods for the approximate solution of integral equations of the first kind*, Proceedings of the Fifth Manitoba Conference on Numerical Mathematics (Univ. Manitoba, Winnipeg, Man., 1975) Congressus Numerantium, No. XVI, Utilitas Math. Publ., Winnipeg, Man., 1976, pp. 3–23. MR**0411213** - R. J. Duffin,
*Algorithms for classical stability problems*, SIAM Rev.**11**(1969), 196–213. MR**249740**, DOI 10.1137/1011034
H. Freeman, - Charles J. Gladwin,
*Quadrature rule methods for Volterra integral equations of the first kind*, Math. Comp.**33**(1979), no. 146, 705–716. MR**521284**, DOI 10.1090/S0025-5718-1979-0521284-2
C. J. Gladwin, - 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 - Peter Henrici,
*Discrete variable methods in ordinary differential equations*, John Wiley & Sons, Inc., New York-London, 1962. MR**0135729** - P. A. W. Holyhead, S. McKee, and P. J. Taylor,
*Multistep methods for solving linear Volterra integral equations of the first kind*, SIAM J. Numer. Anal.**12**(1975), no. 5, 698–711. MR**413564**, DOI 10.1137/0712052 - P. A. W. Holyhead and S. McKee,
*Stability and convergence of multistep methods for linear Volterra integral equations of the first kind*, SIAM J. Numer. Anal.**13**(1976), no. 2, 269–292. MR**471396**, DOI 10.1137/0713026 - 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** - 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** - P. J. Taylor,
*The solution of Volterra integral equations of the first kind using inverted differentiation formulae*, Nordisk Tidskr. Informationsbehandling (BIT)**16**(1976), no. 4, 416–425. MR**433930**, DOI 10.1007/bf01932725 - P. H. M. Wolkenfelt,
*Linear multistep methods and the construction of quadrature formulae for Volterra integral and integro-differential equations*, Mathematisch Centrum, Amsterdam, 1979. Afdeling Numerieke Wiskunde [Department of Numerical Mathematics], 76. MR**569940**

*Finite Differences for Actuarial Students*, Cambridge Univ. Press, Cambridge, 1962, p. 113.

*Numerical Solution of Volterra Integral Equations of the First Kind*, Ph.D. Thesis, Dalhousie Univ., 1975.

## Additional Information

- © Copyright 1982 American Mathematical Society
- Journal: Math. Comp.
**39**(1982), 511-518 - MSC: Primary 65R20; Secondary 45D05, 45L10
- DOI: https://doi.org/10.1090/S0025-5718-1982-0669643-1
- MathSciNet review: 669643