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High-order methods for the numerical solution of Volterra integro- differential equations. (English) Zbl 0634.65143

Author’s summary: If a first-order Volterra integro-differential equation is solved by collocation in the space of continuous polynomial splines of degree \(m\geq 1\), with collocation occurring at the Gauss-Legendre points, then the resulting approximation u converges, at its knots, like \(O(h^{2m})\), while its derivative u’ exhibits only O(h m)-convergence. This paper deals with the question of how to choose the collocation points so that both u and u’ converge like \(O(h^{q\quad *})\), with q * maximal.
Reviewer: Z.Jackiewicz

MSC:

65R20 Numerical methods for integral equations
45J05 Integro-ordinary differential equations
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