Elvira Russo - Academia.edu (original) (raw)
Papers by Elvira Russo
Applied Mathematics Letters, 2010
In this letter, a Painlevé integrable coupled KdV equation is proved to be also Lax integrable by... more In this letter, a Painlevé integrable coupled KdV equation is proved to be also Lax integrable by a prolongation technique. The Miura transformation and the corresponding coupled modified KdV equation associated with this equation are derived.
ber die Stabilität des exakten Einschritt-Kollokationsverfahrens für Volterrasche Integralgleichungen zweiter Art mit degeneriertem Kern
Computing, 1988
The local stability properties of the collocation method applied to a second kind Volterra integr... more 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. Es 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.
Analyse der globalen Stabilität von Runge-Kutta Methoden für Volterrasche Integral und Integral-Differentialgleichungen mit degeneriertem Kern
Computing, 1990
We investigate the stability of the numerical solutions resulting from applying very general clas... more 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. Wir 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.
On the stability of the one-step exact collocation methods for the numerical solution of the second kind Volterra integral equation
Bit Numerical Mathematics, 1989
The purpose of this paper is to analyze the stability properties of one-step collocation methods ... more The purpose of this paper is to analyze the stability properties of one-step collocation methods for the second kind Volterra integral equation through application to the basic test and the convolution test equation. Stability regions are determined when the collocation parameters are symmetric and when they are zeros of ultraspherical polynomials.
Journal of Mathematical Analysis and Applications, 1997
Investigation of the boundedness of the solutions of Volterra equations with discrete time by mea... more Investigation of the boundedness of the solutions of Volterra equations with discrete time by means of the direct Liapunov method and comparison theorems is performed. Boundedness conditions of solutions of some particular classes of equations are derived. Using such conditions, stability of Direct Quadrature methods for second kind Volterra equations is analyzed. ᮊ
Periodic Solution of Whole Line Difference Equations
Journal of Difference Equations and Applications, 2004
We introduce a general reduction method for the study of periodic points near a fixed point in a ... more We introduce a general reduction method for the study of periodic points near a fixed point in a family of reversible diffeomorphisms. We impose no restrictions on the linearization at the fixed point except invertibility, allowing higher multiplicities. It is shown that the problem reduces to a similar problem for a reduced family of diffeomorphisms, which is itself reversible, but also has an additional q -symmetry. The reversibility in combination with the q -symmetry translates to a q -symmetry for the problem, which allows to write down the bifurcation equations. Moreover, the reduced family can be calculated up to any order by a normal form reduction on the original system. The method of proof combines normal forms with the Lyapunov–Schmidt method, and makes repetitive use of the Implicit Function Theorem. As an application we analyze the branching of periodic points near a fixed point in a family of reversible mappings, when for a critical value of the parameters the linearization at the fixed point has either a pair of simple purely imaginary eigenvalues that are roots of unity or a pair of non-semisimple purely imaginary eigenvalues that are roots of unity with algebraic multiplicity 2 and geometric multiplicity 1.
Nonstationary Waveform Relaxation Methods for Abel Integral Equations
Journal of Integral Equations and Applications, 2004
Global stability analysis of the Runge-Kutta methods for volterra integral and integro-differential equations with degenerate kernels
Computing, 1990
We investigate the stability of the numerical solutions resulting from applying very general clas... more 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. Wir 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.
Computing, 1988
The local stability properties of the collocation method applied to a second kind Volterra integr... more 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. Es 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.
Mathematics and Computers in Simulation, 2011
Numerical solution of two delays Volterra Integral Equations is considered and the stability is s... more Numerical solution of two delays Volterra Integral Equations is considered and the stability is studied on a nonlinear test equation by carrying out a parallel investigation both on the continuous and the discrete problem.
Applied Mathematics and Computation
We analyze stability of equilibria for a delayed SIR epidemic model, in which population growth i... more We analyze stability of equilibria for a delayed SIR epidemic model, in which population growth is subject to logistic growth in absence of disease, with a nonlinear incidence rate satisfying suitable monotonicity conditions. The model admits a unique endemic equilibrium if and only if the basic reproduction number R 0 exceeds one, while the trivial equilibrium and the disease-free equilibrium always exist. First we show that the disease-free equilibrium is globally asymptotically stable if and only if R 0 ≤ 1. Second we show that the model is permanent and it has a unique endemic equilibrium if and only if R 0 > 1. Moreover, using a threshold parameter R 0 characterized by the nonlinear incidence function, we establish that the endemic equilibrium is locally asymptotically stable for 1 < R 0 ≤ R 0 and it loses stability as the length of the delay increases past a critical value for 1 < R 0 < R 0 . Our result is an extension of the stability results in [J-J. Wang, J-Z. Zhang, Z. Jin, Analysis of an SIR model with bilinear incidence rate, Nonl. Anal. RWA. 11 (2009RWA. 11 ( ) 2390RWA. 11 ( -2402.
Applied Mathematics Letters, 2010
In this letter, a Painlevé integrable coupled KdV equation is proved to be also Lax integrable by... more In this letter, a Painlevé integrable coupled KdV equation is proved to be also Lax integrable by a prolongation technique. The Miura transformation and the corresponding coupled modified KdV equation associated with this equation are derived.
ber die Stabilität des exakten Einschritt-Kollokationsverfahrens für Volterrasche Integralgleichungen zweiter Art mit degeneriertem Kern
Computing, 1988
The local stability properties of the collocation method applied to a second kind Volterra integr... more 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. Es 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.
Analyse der globalen Stabilität von Runge-Kutta Methoden für Volterrasche Integral und Integral-Differentialgleichungen mit degeneriertem Kern
Computing, 1990
We investigate the stability of the numerical solutions resulting from applying very general clas... more 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. Wir 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.
On the stability of the one-step exact collocation methods for the numerical solution of the second kind Volterra integral equation
Bit Numerical Mathematics, 1989
The purpose of this paper is to analyze the stability properties of one-step collocation methods ... more The purpose of this paper is to analyze the stability properties of one-step collocation methods for the second kind Volterra integral equation through application to the basic test and the convolution test equation. Stability regions are determined when the collocation parameters are symmetric and when they are zeros of ultraspherical polynomials.
Journal of Mathematical Analysis and Applications, 1997
Investigation of the boundedness of the solutions of Volterra equations with discrete time by mea... more Investigation of the boundedness of the solutions of Volterra equations with discrete time by means of the direct Liapunov method and comparison theorems is performed. Boundedness conditions of solutions of some particular classes of equations are derived. Using such conditions, stability of Direct Quadrature methods for second kind Volterra equations is analyzed. ᮊ
Periodic Solution of Whole Line Difference Equations
Journal of Difference Equations and Applications, 2004
We introduce a general reduction method for the study of periodic points near a fixed point in a ... more We introduce a general reduction method for the study of periodic points near a fixed point in a family of reversible diffeomorphisms. We impose no restrictions on the linearization at the fixed point except invertibility, allowing higher multiplicities. It is shown that the problem reduces to a similar problem for a reduced family of diffeomorphisms, which is itself reversible, but also has an additional q -symmetry. The reversibility in combination with the q -symmetry translates to a q -symmetry for the problem, which allows to write down the bifurcation equations. Moreover, the reduced family can be calculated up to any order by a normal form reduction on the original system. The method of proof combines normal forms with the Lyapunov–Schmidt method, and makes repetitive use of the Implicit Function Theorem. As an application we analyze the branching of periodic points near a fixed point in a family of reversible mappings, when for a critical value of the parameters the linearization at the fixed point has either a pair of simple purely imaginary eigenvalues that are roots of unity or a pair of non-semisimple purely imaginary eigenvalues that are roots of unity with algebraic multiplicity 2 and geometric multiplicity 1.
Nonstationary Waveform Relaxation Methods for Abel Integral Equations
Journal of Integral Equations and Applications, 2004
Global stability analysis of the Runge-Kutta methods for volterra integral and integro-differential equations with degenerate kernels
Computing, 1990
We investigate the stability of the numerical solutions resulting from applying very general clas... more 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. Wir 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.
Computing, 1988
The local stability properties of the collocation method applied to a second kind Volterra integr... more 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. Es 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.
Mathematics and Computers in Simulation, 2011
Numerical solution of two delays Volterra Integral Equations is considered and the stability is s... more Numerical solution of two delays Volterra Integral Equations is considered and the stability is studied on a nonlinear test equation by carrying out a parallel investigation both on the continuous and the discrete problem.
Applied Mathematics and Computation
We analyze stability of equilibria for a delayed SIR epidemic model, in which population growth i... more We analyze stability of equilibria for a delayed SIR epidemic model, in which population growth is subject to logistic growth in absence of disease, with a nonlinear incidence rate satisfying suitable monotonicity conditions. The model admits a unique endemic equilibrium if and only if the basic reproduction number R 0 exceeds one, while the trivial equilibrium and the disease-free equilibrium always exist. First we show that the disease-free equilibrium is globally asymptotically stable if and only if R 0 ≤ 1. Second we show that the model is permanent and it has a unique endemic equilibrium if and only if R 0 > 1. Moreover, using a threshold parameter R 0 characterized by the nonlinear incidence function, we establish that the endemic equilibrium is locally asymptotically stable for 1 < R 0 ≤ R 0 and it loses stability as the length of the delay increases past a critical value for 1 < R 0 < R 0 . Our result is an extension of the stability results in [J-J. Wang, J-Z. Zhang, Z. Jin, Analysis of an SIR model with bilinear incidence rate, Nonl. Anal. RWA. 11 (2009RWA. 11 ( ) 2390RWA. 11 ( -2402.