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Mathematics of Computation

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Implicit Runge-Kutta methods of optimal order for Volterra integro-differential equations

Author: Hermann Brunner
Journal: Math. Comp. 42 (1984), 95-109
MSC: Primary 65R20; Secondary 45J05, 45L10
MathSciNet review: 725986
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Abstract: Implicit Runge-Kutta methods with m stages and optimal order $ p = 2m$ for the approximate solution of Volterra integro-differential equations can be viewed as fully discretized collocation methods in certain polynomial spline spaces. The choice of the quadrature formulas needed for the full discretization of the collocations is investigated, and it is shown that, in contrast to ordinary differential equations, there exist (for fixed m) several optimal methods.

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Keywords: Volterra integro-differential equations, collocation methods, implicit Runge-Kutta methods of optimal order
Article copyright: © Copyright 1984 American Mathematical Society