Stability Analysis of Runge-Kutta Methods for Volterra Integral Equations of the Second Kind
Open Access
- 1 January 1990
- journal article
- Published by Oxford University Press (OUP) in IMA Journal of Numerical Analysis
- Vol. 10 (1) , 103-118
- https://doi.org/10.1093/imanum/10.1.103
Abstract
Stability analysis of Volterra-Runge-Kutta methods based on the basic test equation of the form where λ is a complex parameter, and on the convolution test equation where λ and σ are real parameters, is presented. General stability conditions are derived and applied to construct numerical methods with good stability properties. In particular, a family of second-order Vo-stable Volterra-Runge-Kutta methods is obtained. No Vo-stable methods of order greater than one have been presented previously in the literature.Keywords
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