Volterra integral equations with periodic solution model a number of periodic phenomena with memory, e.g. the spread of seasonal epidemics. An efficient and accurate numerical solution of these equations may be found by means of special purpose methods, which exploit the a priori knowledge of the qualitative behavior of the solution. On this direction, we propose exponentially-fitted direct quadrature methods of high order. The coefficients of these methods depend on the frequency of the problem, to reduce the error when periodic problems are treated and an estimate of the frequency is available. In this poster we present the construction and analysis of these methods, and illustrate their performances on some significant test problems. REFERENCES [1] A. Cardone, L.Gr. Ixaru and B. Paternoster. Exponential fitting direct quadrature methods for Volterra integral equations. Numer. Algorithms, 55 (4), 2010, 467 – 480. [2] A. Cardone, L.Gr. Ixaru, B. Paternoster and G. Santomauro. Ef-Gaussian direct quadrature methods for Volterra integral equations with periodic solution. Math. Comput. Simul., 110 2015, 125 – 143. [3] L.Gr. Ixaru and G. Vanden Berghe. Exponential fitting. Kluwer Academic Publishers, Dordrecht, 2004.
High order exponentially fitted methods for periodic Volterra integral equations
CARDONE, Angelamaria;D'AMBROSIO, RAFFAELE;PATERNOSTER, Beatrice
2015
Abstract
Volterra integral equations with periodic solution model a number of periodic phenomena with memory, e.g. the spread of seasonal epidemics. An efficient and accurate numerical solution of these equations may be found by means of special purpose methods, which exploit the a priori knowledge of the qualitative behavior of the solution. On this direction, we propose exponentially-fitted direct quadrature methods of high order. The coefficients of these methods depend on the frequency of the problem, to reduce the error when periodic problems are treated and an estimate of the frequency is available. In this poster we present the construction and analysis of these methods, and illustrate their performances on some significant test problems. REFERENCES [1] A. Cardone, L.Gr. Ixaru and B. Paternoster. Exponential fitting direct quadrature methods for Volterra integral equations. Numer. Algorithms, 55 (4), 2010, 467 – 480. [2] A. Cardone, L.Gr. Ixaru, B. Paternoster and G. Santomauro. Ef-Gaussian direct quadrature methods for Volterra integral equations with periodic solution. Math. Comput. Simul., 110 2015, 125 – 143. [3] L.Gr. Ixaru and G. Vanden Berghe. Exponential fitting. Kluwer Academic Publishers, Dordrecht, 2004.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
