177,109 research outputs found
Pseudospectral differencing methods for characteristic roots of delay differential equations
No full textIn [D. Breda, S. Maset, and R. Vermiglio, IMA J. Numer. Anal., 24 (2004), pp. 1– 19.] and [D. Breda, The Infinitesimal Generator Approach for the Computation of Characteristic Roots for Delay Differential Equations Using BDF Methods, Research report UDMI RR17/2002, Dipartimento di Matematica e Informatica, Universit`a degli Studi di Udine, Udine, Italy, 2002.] the authors proposed to compute the characteristic roots of delay differential equations (DDEs) with multiple discrete and distributed delays by approximating the derivative in the infinitesimal generator of the solution operator semigroup by Runge–Kutta (RK) and linear multistep (LMS) methods, respectively. In this work the same approach is proposed in a new version based on pseudospectral differencing techniques. We prove the “spectral accuracy” convergence behavior typical of pseudospectral schemes, as also illustrated by some numerical experiments
Realtà e Modelli
No full textTra le varie proposte presenti nel libro, il laboratorio “Realtà e modelli” vuole evidenziare il ruolo chiave della matematica nella modellizzazione di fenomeni reali, puntando anche a sviluppare un’attitudine sperimentale verso la disciplina. Presenta le attività svolte con gli studenti delle scuole superiori relative alla descrizione e allo studio qualitativo e numerico di alcuni semplici modelli matematici che si incontrano nella fisica e nella biologia e che sono descritti da equazioni differenziali ordinarie
Pseudospectral differencing methods for characteristic roots of delay differential equations
No full textIn [D. Breda, S. Maset, and R. Vermiglio, IMA J. Numer. Anal., 24 (2004), pp. 1--19.] and [D. Breda, The Infinitesimal Generator Approach for the Computation of Characteristic Roots for Delay Differential Equations Using BDF Methods, Research report UDMI RR17/2002, Dipartimento di Matematica e Informatica, Università degli Studi di Udine, Udine, Italy, 2002.] the authors proposed to compute the characteristic roots of delay differential equations (DDEs) with multiple discrete and distributed delays by approximating the derivative in the infinitesimal generator of the solution operator semigroup by Runge--Kutta (RK) and linear multistep (LMS) methods, respectively. In this work the same approach is proposed in a new version based on pseudospectral differencing techniques. We prove the "spectral accuracy" convergence behavior typical of pseudospectral schemes, as also illustrated by some numerical experiments
Computing Multivariate Process Capability Indices With Microsoft Excel
No full textIn manufacturing industry there is growing interest in measures of process capability under multivariate setting. While there are many statistical packages to assess univariate capability, a current problem with the multivariate measures of capability is the shortage of user friendly software. In this paper a Visual Basic program has been developed to realize an Excel spreadsheet that may be used to compute two multivariate measures of capability. Our aim is to provide a useful tool for practitioners dealing with multivariate capability assessment problems. The features of the program include easy data entry and clear report format
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
On the stability of continuous quadrature rules for differential equatons with several delays
No full textMultistep high order interpolants of Runge-Kutta methods
No full textWe consider a p-order Runge-Kutta method K(i)(n) = f(x(n) + c(i)h, y(n) + hSIGMA(j=1)(nu)a(ij)K(j)(n)), i = 1,..., nu, y(n+1) = y(n) + hSIGMA(i = 1)(nu)b(i)K(i)(n)), for solving an initial-value problem for ordinary differential equations. The aim of this paper is to construct p-order interpolants by using the values furnished by the method on N successive intervals of integration. By using Lagrange interpolation one can obtain a p-order interpolant over p intervals, but we are interested in finding the minimum number of intervals needed to obtain this. We provide the conditions to be satisfied and we obtain an estimation of the number N. Some examples are given
A Stable Numerical Approach for Implicit Non-Linear Neutral Delay Differential Equations
No full textIn this paper we consider implicit non-linear neutral delay differential equations to derive efficient numerical schemes with good stability properties. The basic idea is to reformulate the original problem eliminating the dependence on the derivative of the solution in the past values. Our hypothesis on the original equation allow us to study the boundedness and asymptotic stability of the true and numerical solutions by the theory of stability with respect to the forcing term
Regularity properties of Runge-Kutta methods for ordinary differential equations
No full textWe investigate the conditions which guarantee that Runge-Kutta methods preserve asymptotic values of the systems of ordinary differential equations. A complete characterization of such methods is given and examples of methods with these properties are presented for s = p = 2. 3 and 4, where s is the number of stages and p is the order of the method
Multistep natural continuous extensions of Runge-Kutta methods: the potential for stable interpolation
No full textThe present paper develops a theory of multistep natural continuous extensions of Runge-Kutta methods, that is interpolants of multistep type that generalize the notion of natural continuous extension introduced by Zennaro [15]. The main motivation for the definition of such a type of interpolants is given by the need for interpolation procedures with strong stability properties and high order of accuracy, in view of interesting applications to the numerical solution of delay differential equations and to the waveform relaxation methods for large systems of ordinary differential equations
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