Maria Rosaria Crisci

Stability of discrete volterra equations of hammerstein type

Stability conditions for Volterra equations with discrete time are obtained using direct Liapunov method, without usual assumption of the summability of the series of the coeffcients. Using such conditions, the stability of some numerical methods for second kind Volterra integral equation is analyzed.

Stability analysis of discrete recurrence equations of Volterra type with degenerate kernels

Abstract Stability criteria are derived for difference equations of Volterra type with degenerate kernels. The main tool in this analysis is the use of the new representation formula which allows us to express the solution of discrete Volterra equation with degenerate kernel in terms of the fundamental matrix of the corresponding first-order system of the difference equations.

On the exponential stability of discrete volterra systems

In this paper necessary and sufficient conditions for the exponential stability of discrete linear Volterra systems are proved. Sufficient conditions, expressed directly in terms of the coefficients, are derived

On the stability of the one-step exact collocation method for the second kind Volterra integral equation with degenerate kernel

The local stability properties of the collocation method applied to a second kind Volterra integral equation with degenerate kernel are investigated.A finite length recurrence relation is derived and theorems for the local stability of the methods are proved.ZusammenfassungEs werden die lokalen Stabilitätseigenschaften der Kollokationsmethode, angewandt auf Volterrasche Integralgleichungen zweiter Art mit degeneriertem Kern, untersucht.Eine Rekursionsrelation endlicher Ordnung wird angegeben, und es werden Sätze über die lokale Stabilität der Methode bewiesen.

Global stability analysis of the Runge-Kutta methods for Volterra integral and integro-differential equations with degenerate kernels

We investigate the stability of the numerical solutions resulting from applying very general classes of Runge-Kutta methods to Volterra integral and integro-differential equations with degenerate kernels. The results are generalizations of previous results obtained by the authors for exact collocation methods for these equations.ZusammenfassungWir untersuchen die Stabilität der numerischen Lösung von Volterraschen Integral- und Integral-Differentialgleichungen mit degeneriertem Kern mit Hilfe von ganz allgemeinen Klassen von Runge-Kutta Methoden. Die Resultate sind Verallgemeinerungen früherer Resultate, die von den Autoren für die exakte Kollokationsmethode für diese Gleichungen erhalten worden sind.