The aim of our research is the construction of efficient and accurate numerical methods for the solution of Volterra Integro-Differential Equations (VIDEs). In order to increase the order of convergence of classical one-step collocation methods, we propose multistep collocation methods, which have been successfully introduced for Volterra integral equations in [1; 2]. Moreover, they are continuous methods, i.e. they furnish an approximation of the solution at each point of the time interval. In this talk we describe the derivation of multistep collocation methods for VIDEs and the analysis of convergence and stability properties. We show some examples of methods which compare favorably with respect to existing one-step methods. This is a joint work with B. Paternoster and D. Conte from University of Salerno. REFERENCES [1] D. Conte, Z. Jackiewicz, B. Paternoster. Two-step almost collocation methods for Volterra integral equations. Appl. Math. Comput., 204 :839{853, 2008. [2] D. Conte, B. Paternoster. Multistep collocation methods for Volterra Integral Equations. Appl. Math. Comput., 59 :1721-1736, 2009.
Continuous numerical methods for Volterra Integro-Differential Equations
CARDONE, Angelamaria;CONTE, Dajana
2011-01-01
Abstract
The aim of our research is the construction of efficient and accurate numerical methods for the solution of Volterra Integro-Differential Equations (VIDEs). In order to increase the order of convergence of classical one-step collocation methods, we propose multistep collocation methods, which have been successfully introduced for Volterra integral equations in [1; 2]. Moreover, they are continuous methods, i.e. they furnish an approximation of the solution at each point of the time interval. In this talk we describe the derivation of multistep collocation methods for VIDEs and the analysis of convergence and stability properties. We show some examples of methods which compare favorably with respect to existing one-step methods. This is a joint work with B. Paternoster and D. Conte from University of Salerno. REFERENCES [1] D. Conte, Z. Jackiewicz, B. Paternoster. Two-step almost collocation methods for Volterra integral equations. Appl. Math. Comput., 204 :839{853, 2008. [2] D. Conte, B. Paternoster. Multistep collocation methods for Volterra Integral Equations. Appl. Math. Comput., 59 :1721-1736, 2009.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
