1,721,003 research outputs found
On the stability of continuous quadrature rules for differential equatons with several delays
No full textPreface to Stability of linear delay differential equations: A numerical approach with MATLAB
No full textComputing the eigenvalues of Gurtin–MacCamy models with diffusion
No full textComputing the eigenvalues of Gurtin–MacCamy models with diffusio
Numerical approximation of characteristic values of Partial Retarded Functional Differential Equations
No full textThe stability of an equilibrium point of a dynamical system is determinedby the position in the complex plane of the so-called characteristic values of the linearizationaround the equilibrium. This paper presents an approach for the computationof characteristic values of partial differential equations of evolution involving timedelay, which is based on a pseudospectral method coupled with a spectral method.The convergence of the computed characteristic values is of infinite order with respectto the pseudospectral discretization and of finite order with respect to the spectralone. However, for one dimensional reaction diffusion equations, the finite order of thespectral discretization is proved to be so high that the convergence turns out to be asfast as one of infinite order
Numerical recipes for investigating endemic equilibria of age-structured SIR epidemics
No full textThe subject of this paper is the analysis of the equibria of a SIR
type epidemic model, which is taken as a case study among the wide family
of dynamical systems of infinite dimension. For this class of systems both
the determination of the stationary solutions and the analysis of their local
asymptotic stability are often unattainable theoretically, thus requiring the
application of existing numerical tools and/or the development of new ones.
Therefore, rather than devoting our attention to the SIR model’s features, its
biological and physical interpretation or its theoretical mathematical analysis,
the main purpose here is to discuss how to study its equilibria numerically, es-
pecially as far as their stability is concerned. To this end, we briefly analyze the
construction and solution of the system of nonlinear algebraic equations lead-
ing to the stationary solutions, and then concentrate on two numerical recipes
for approximating the stability determining values known as the characteristic
roots. An algorithm for the purpose is given in full detail. Two applications
are presented and discussed in order to show the kind of results that can be
obtained with these tools
Numerical computation of characteristic multipliers for linear time periodic coefficients delay differential equations
No full textNumerical computation of characteristic multipliers for linear time periodic coefficients delay differential equation
An adaptive algorithm for efficient computation of level curves of surfaces
No full textAn adaptive algorithm for efficient computation of level curves of surface
Efficient computation of stability charts for linear time delay systems
No full textEfficient computation of stability charts for linear time delay system
Regularity properties of multistage integration methods
No full textThe numerical method for ordinary differential equations is regular if it has the same set of finite asymptotic values as the underlying differential system. This paper examines the regularity and strong regularity properties of diagonally implicit multistage integration methods (DIMSIMs) introduced recently by J.C. Butcher. A sufficient condition for regularity and strong regularity of such methods of any order is given and it is proved that this condition is also necessary for two-step two-stage DIMSIMs of order greater than or equal to two. It is also demonstrated that there exist regular schemes in the class of explicit DIMSIMs. This is in contrast to explicit Runge-Kutta methods with more than one stage, which are always irregular
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