Abstract
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.
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Partially supported by the School of Sciences and Technology - University of Naples “Federico II” under the project “F.A.R.O.” Control and stability of diffusive processes in the environment.
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Conte, D., D’Ambrosio, R., Izzo, G. et al. Natural Volterra Runge-Kutta methods. Numer Algor 65, 421–445 (2014). https://doi.org/10.1007/s11075-013-9790-z
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DOI: https://doi.org/10.1007/s11075-013-9790-z
Keywords
- Volterra integral equation
- Volterra Runge-Kutta methods
- Order and stage order conditions
- Stability analysis
- A-stability
- V 0-stability