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 stability problems*, SIAM Rev.**11**(1969), 196–213. MR**0249740**, https://doi.org/10.1137/1011034**[2]**Peter Henrici,*Discrete variable methods in ordinary differential equations*, John Wiley & Sons, Inc., New York-London, 1962. MR**0135729****[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**, https://doi.org/10.1090/S0025-5718-1982-0669643-1**[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**, https://doi.org/10.1090/S0025-5718-1979-0521284-2**[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****[7]**Morris Marden,*Geometry of polynomials*, Second edition. Mathematical Surveys, No. 3, American Mathematical Society, Providence, R.I., 1966. MR**0225972****[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