1,721,002 research outputs found
A regularizing parameter for some Fredholm integral equations
No full textThe regularizing parameter appearing in some Fredholm integral equations of the second kind is discussed. Theoretical estimates and the results of numerical tests confirming the theoretical expectations are given. 2000 Mathematics Subject Classification: 65R20; 45E0
Weighted convergence of some positive linear operators on the real semiaxis
No full textSome Shepard and Gr ̈unwald type operators are introduced on the semiaxis and their convergence, in suitable weighted spaces equipped with the uniform norm, is investigated
A quadrature method for Cauchy singular integral equations with singular given functions
No full textOn a positive linear operator on the semiaxis
No full textA positive linear operator is introduced on the semiaxis and its convergence is investigated in suitable weighted spaces equipped with the uniform and the L1-norm. As corollaries, error estimates for a special Hermite-Fejer polynomial are obtained
Metodi Numerici per la Matematica Applicata
No full textLa matematica, a partire dalla modellizzazione dei fenomeni fisici, sino al calcolo numerico ed alla simulazione di processi, ha sempre giocato un ruolo fondamentale nelle scienze applicate e, in particolare, in molti settori dell'Ingegneria. Questo libro si propone di far acquisire ai lettori interessati una conoscenza operativa di basilari metodologie sia numeriche, sia analitiche, tipiche della matematica applicata e computazionale. Gli argomenti trattati nel libro, nel loro complesso, rappresentano strumenti di uso corrente nella teoria del controllo, nell'analisi dei segnali, nella bioingegneria, nelle telecomunicazioni, nello studio dei campi elettromagnetici, nell'analisi di modelli elettrici e di processi chimici, nell'analisi della risposta del sistema immunitario ad agenti virali e in numerosi altri settori applicativi
Nystrom methods for weakly singularFredholm integral equationswith singular right-hand sides
No full textA global method for solving second-kind Volterra–Fredholm integral equations
Full text linkThe paper presents a Nyström-type method to approximate the solution of second-kind Volterra–Fredholm integral equations. Two forms are considered, that is the disjoint form, in which the Volterra and Fredholm operators are additive integrals; and the mixed one, in which the two integrals appear in a single term through composition. In both situations, the right-hand side and the kernel functions may have algebraic singularities at ±1 and hence equations are treated in suitable weighted spaces equipped with the uniform norm. The proposed methods, based on product and Gauss rules, are stable and convergent. The error is of the order of the best polynomial approximation of the given functions. Numerical examples are presented to illustrate the accuracy of the method
A Nyström method for a boundary integral equation related to the Dirichlet problem on domains with corners
No full textThe authors consider the interior Dirichlet problem for Laplace’s equation on planar domains with corners. They provide a complete analysis of a natural method of Nyström type based on the global Gauss–Lobatto quadrature rule, in order to approximate the solution of the corresponding double layer boundary integral equation. Mellin-type integral operators are involved and, as usual, a modification of the method close to the corners is needed. A new modification is proposed and the convergence and stability of the “modified” quadrature method are proved. Some numerical tests are also included
A fully-discrete-state kinetic theory approach to traffic flow on road networks
Full text linkThis paper presents a new approach to the modeling of vehicular traffic flows on road networks based on kinetic equations. While in the literature the problem has been extensively studied by means of macroscopic hydrodynamic models, to date there are still not, to the authors' knowledge, contributions tackling it from a genuine statistical mechanics point of view. Probably one of the reasons is the higher technical complexity of kinetic traffic models, further increased in case of several interconnected roads. Here such difficulties of the theory are overcome by taking advantage of a discrete structure of the space of microscopic states of the vehicles, which is also significant in view of including the intrinsic microscopic granularity of the system in the mesoscopic representation
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