Taylor series methods for the solution of Volterra integral and integro-differential equations

Author:
Alan Goldfine

Journal:
Math. Comp. **31** (1977), 691-707

MSC:
Primary 65R05

DOI:
https://doi.org/10.1090/S0025-5718-1977-0440970-4

MathSciNet review:
0440970

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Abstract | References | Similar Articles | Additional Information

Abstract: Algorithms based on the use of Taylor series are developed for the numerical solution of Volterra integral and integro-differential equations of arbitrary order. It is shown that these algorithms are uniformly convergent, bounds are obtained for the truncation error, and an asymptotic error analysis is provided for the integral equation case. The various problems of computer implementation are discussed, and the results of certain experiments suggested by the theory are presented.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1977-0440970-4

Keywords:
Volterra integral equation,
Volterra integro-differential equation,
Taylor series method,
initial value problems,
symbolic differentiation

Article copyright:
© Copyright 1977
American Mathematical Society