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Global stability analysis of the Runge-Kutta methods for volterra integral and integro-differential equations with degenerate kernels
19/19 checkable references clean · checked 2026-08-10
Every reference with a DOI in the deposited reference list resolved to a known work in Crossref or DataCite at the dated check, and none carried a retraction, withdrawal, or removal notice.
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The 19 checked references that resolve
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Stability analysis of certain Runge-Kutta procedures for Volterra integral equations
resolves10.1137/0716066
Regions of Stability in the Numerical Treatment of Volterra Integro-Differential Equations
resolves10.1090/S0025-5718-1989-0971402-3
Natural continuous extensions of Runge-Kutta methods for Volterra integral equations of the second kind and their applications
resolves10.1090/S0025-5718-1984-0725986-6
Implicit Runge-Kutta methods of optimal order for Volterra integro-differential equations
resolves10.1016/0377-0427(86)90221-9
High-order methods for the numerical solution of Volterra integro-differential equations
resolves10.1090/S0025-5718-1982-0658219-8
Runge-Kutta theory for Volterra integral equations of the second kind
resolves10.1216/JIE-1989-2-1-49
Global stability condition for collocation methods for volterra integral equations of the second kind ByM.R. Crisci, Z. Jackiewicz, E. Russo and A Vecchio
resolves10.1090/S0025-5718-1992-1106963-7
Stability results for one-step discretized collocation methods in the numerical treatment of Volterra integral equations
resolves10.1016/0377-0427(90)90015-R
Stability analysis of the de Hoog and Weiss implicit Runge-Kutta methods for the Volterra integral and integrodifferential equations
resolves10.1007/BF02276915
On the stability of the one-step exact collocation method for the second kind volterra integral equation with degenerate kernel
resolves10.1137/0720037
Order of Convergence of One-Step Methods for Volterra Integral Equations of the Second Kind
resolves10.1090/S0025-5718-1983-0701626-6
Runge-Kutta theory for Volterra and Abel integral equations of the second kind
resolves10.1093/imanum/3.4.439
On the Stability of Linear Multistep Methods for Volterra Convolution Equations
resolves10.1007/BF01932780
Convergence and stability results in Runge-Kutta type methods for Volterra integral equations of the second kind
resolves10.1093/imanum/1.3.303
Convergence and Stability Analysis for Modified Runge—Kutta Methods in the Numerical Treatment of Second-Kind Volterra Integral Equations
resolves10.1007/BF01396328
Natural Continuous Extensions of Runge-Kutta methods for Volterra integrodifferential equations
The 9 references without a DOI — listed, not checked
no DOI — not checkedBellen, A., Jackiewicz, Z., Vermiglio, R., Zennaro, M.: Stability analysis of Runge-Kutta methods for Volterra integral equations of the second kind. Submitted.
no DOI — not checkedBellen, A., Jackiewicz, Z., Zennaro, M.: A necessary condition for stability of Volterra-Runge-Kutta methods. Report 65R20-8, University of Arkansas, Fayetteville 1987.
no DOI — not checkedBel'tyukov, B. A.: An analog of the Runge-Kutta method for solution of nonlinear Volterra type integral equations. Differencial'nye Uravnenija1, 545–556 (1965).
no DOI — not checkedBownds, J. M., Cushing, J. M.: Some stability criteria for linear systems of Volterra integral equations. Funkcial. Ekvac.15, 101–117 (1972).
no DOI — not checkedBrunner, H., van der Houwen, P. J.: The numerical solution of Volterra equations. Amsterdam: North Holland. 1986.
no DOI — not checkedCrisci, M. R., Jackiewicz, Z., Russo, E., Vecchio, A.: Global stability of exact collocation methods for Volterra integro-differential equations. Atti. Sem. Mat. Fis. Univ. Modena. (To appear)
no DOI — not checkedCrisci, M. R., Russo, E., Vecchio, A.: Stability of the collocation methods for the Volterra integro-differential equation IAM CNR Techn. Rep. 46/88 1988.
no DOI — not checkedCrisci, M. R., Jackiewicz, Z., Russo, E., Vecchio, A.: Boundedness of Runge-Kutta solutions to Volterra integral and integro-differential equations with degenerate kernels. Report 120. Tempe: Arizona State University. (1988).
no DOI — not checkedPouzet, P.: Etude en vue de Leur traitement numerique des equations integrales de type Volterra. Rev. Francais Traitement Information (Chiffres)6, 79–112 (1963).
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