1,721,035 research outputs found
Aspetti paralleli per l'integrazione numericadi problemi ai valori iniziali per equazioni differenzialiordinarie del secondo ordine di forma speciale
No full textNumerical simulation of a SIS epidemic model based on a nonlinear Volterra integral equation
No full textWe consider a SIS epidemic model based on a Volterra integral equation and we compare the dynamical behavior of the analytical solution and its numerical approximation obtained by direct quadrature methods. We prove that, under suitable assumptions, the numerical scheme preserves the qualitative properties of the continuous equation and we show that, as the stepsize tends to zero, the numerical bifurcation points tend to the continuous one
Numerical analysis of nonlinear Volterra integral equations: stability with respect to bounded perturbations
No full text
Nonlinear stability of direct quadrature methods for Volterra integral equations
No full textAn important topic in the numerical analysis of Volterra integral equations is the stability theory. The main results known in the literature have been obtained on linear test equations or, at least, on nonlinear equations with convolution kernel. Here, we consider Volterra integral equations with Hammerstein nonlinearity, not necessarily of convolution type, and we study the error equation for Direct Quadrature methods with respect to bounded perturbations. For a class of Direct Quadrature methods, we obtain conditions on the stepsize h for the numerical solution to behave stably and we report numerical examples which show the robustness of this nonlinear stability theory
A sufficient condition for the stability of direct quadrature methods for Volterra integral equations
No full textWithin the theoretical framework of the numerical stability analysis for the
Volterra integral equations, we consider a new class of test problems and we study the
long-time behavior of the numerical solution obtained by direct quadrature methods
as a function of the stepsize. Furthermore, we analyze how the numerical solution
responds to certain perturbations in the kernel
Stability and boundedness of numerical approximations to Volterra integral equations
No full textVolterra Integral Equations (VIEs) arise in many problems of real life, as, for example, feedback control theory, population dynamics and fluid dynamics. A reliable numerical simulation of these phenomena requires a careful analysis of the long time behavior of the numerical solution. Here we develop a numerical stability theory for Direct Quadrature (DQ) methods which applies to a quite general and representative class of problems. We obtain stability results under some conditions on the stepsize and, in particular cases, unconditional stability for DQ methods of whatever order
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