TY - JOUR
T1 - Stability analysis of runge-kutta methods for volterra integral equations of the second kind
AU - Bellen, A.
AU - Jackiewicz, Zdzislaw
AU - Vermiglio, R.
AU - Zennaro, M.
N1 - Funding Information:
The work of A. Bellen, R. Venniglio, and M. Zennaro was supported by the Italian Government from MPI funds (40 per cent). The work of Z. Jackiewicz was supported by Consiglio Nazionale delle Ricerche and by the National Science Foundation under grant NSF DMS-8520900.
PY - 1990/1
Y1 - 1990/1
N2 - Stability analysis of Volterra-Runge-Kutta methods based on the basic test equation of the form. y(t)=1+λ∫0ty(s) ds (t≥0),where λ is a complex parameter, and on the convolution test equation. y(t)=1+∫0t[λ+σ(t-s)]y(s)ds (t≥0),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.
AB - Stability analysis of Volterra-Runge-Kutta methods based on the basic test equation of the form. y(t)=1+λ∫0ty(s) ds (t≥0),where λ is a complex parameter, and on the convolution test equation. y(t)=1+∫0t[λ+σ(t-s)]y(s)ds (t≥0),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.
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U2 - 10.1093/imanum/10.1.103
DO - 10.1093/imanum/10.1.103
M3 - Article
AN - SCOPUS:0042858003
SN - 0272-4979
VL - 10
SP - 103
EP - 118
JO - IMA Journal of Numerical Analysis
JF - IMA Journal of Numerical Analysis
IS - 1
ER -