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Order of Convergence of One-Step Methods for Volterra Integral Equations of the Second Kind

Lubich, Christian
Norsett, Syvert Paul
Published in SIAM Journal on Numerical Analysis. 1983, vol. 20, no. 3, p. 569-579
Abstract Nice proofs of convergence and asymptotic expansions are known for one-step methods for ordinary differential equations. It is shown that these proofs can be generalized in a natural way to "extended" one-step methods for Volterra integral equations of the second kind. Furthermore, the convergence of "mixed" one-step methods is investigated. For both types general Volterra-Runge-Kutta methods are considered as examples.
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Deposited on : 2010-11-15

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