Document Zbl 1291.65377

Conte, Dajana; D’Ambrosio, Raffaele; Izzo, Giuseppe; Jackiewicz, Zdzislaw

Natural Volterra Runge-Kutta methods. (English) Zbl 1291.65377

Numer. Algorithms 65, No. 3, 421-445 (2014).

Summary: A very general class of Runge-Kutta methods for Volterra integral equations of the second kind is analyzed. Order and stage order conditions are derived for methods of order \(p\) and stage order \(q=p\) up to the order four. We also investigate stability properties of these methods with respect to the basic and the convolution test equations. The systematic search for \(A\)- and \(V_0\)-stable methods is described and examples of highly stable methods are presented up to the order \(p=4\) and stage order \(q=4\).

Cited in 1 Review

Cited in 14 Documents

MSC:

65R20	Numerical methods for integral equations
45D05	Volterra integral equations
45G10	Other nonlinear integral equations

Keywords:

Volterra integral equation; Volterra Runge-Kutta methods; order and stage order conditions; stability analysis; \(A\)-stability: \(V_0\)-stability; numerical examples

Software:

RODAS

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Full Text: DOI

References:

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