Runge-Kutta theory for Volterra integral equations of the second kind-Reference-Cited by-同舟云学术

Runge-Kutta theory for Volterra integral equations of the second kind

Published:1982 Issue:159 Volume:39 Page:147-163
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Brunner H.,Hairer E.,Nørsett S. P.

Abstract

The present paper develops the theory of general Runge-Kutta methods for Volterra integral equations of the second kind. The order conditions are derived by using the theory of P-series, which for our problem reduces to the theory of V-series. These results are then applied to two special classes of Runge-Kutta methods introduced by Pouzet and by Beĺtyukov.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1982-39-159/S0025-5718-1982-0658219-8/S0025-5718-1982-0658219-8.pdf

Reference14 articles.

1. Sulla risoluzione numerica delle equazioni integrali di Volterra di seconda specie;Aparo, Enzo;Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8),1959

2. Monographs on Numerical Analysis;Baker, Christopher T. H.,1977

3. An analogue of the Runge-Kutta method for the solution of nonlinear integral equations of Volterra type;Bel′tjukov, B. A.;Differencial\cprime nye Uravnenija,1965

4. H. Brunner & S. P. Nørsett, Runge-Kutta Theory for Volterra Integral Equations of the Second Kind, Report 1/80, Dept. of Math., NTH-Trondheim, Norway, 1980.

5. An algebraic theory of integration methods;Butcher, J. C.;Math. Comp.,1972

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