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Some extended explicit Bel’tyukov pairs for Volterra integral equations of the second kind. (English) Zbl 0972.65119
Authors’ abstract: We derive and investigate a family of pairs of extended explicit Bel’tyukov Runge-Kutta (EBVRK) formulas to treat Volterra integral equations of the second kind. Each pair uses six stages and consists of an order 3 formula completely embedded in an order 4 formula. We examine the structure of EBVRK pairs to facilitate their derivation, and in particular, we show that at least six stages are needed to form such pairs. This design is motivated to allow a variable stepsize in order to satisfy a prescribed error tolerance with a minimum of computation. Some numerical examples illustrate the procedures.

MSC:
65R20 Numerical methods for integral equations
45D05 Volterra integral equations
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