Collocation methods for fractional differential equations have been introduced by Blank [1] and later on rigorously analyzed by Pedas and Tamme [3,4]. Recently Cardone, Conte and Paternoster [2] introduced two step collocation methods, which raise the order of convergence, by using additional information from the past, without increasing the computational cost. Here we study the stability of both classes of methods, in order to nd methods with unbounded stability regions. This is a joint work with D. CONTE and B. PATERNOSTER from UNIVERSITY OF SALERNO. [1 ] L. Blank, Numerical treatment of differential equations of fractional order, Nonlinear World, 4 (1997), 473-491. [2 ] A. Cardone, D. Conte, B. Paternoster, Two-step collocation methods forfractional dierential equations, to appear in Discrete Cont.Dyn.-B. [3 ] A. Pedas and E. Tamme, On the convergence of spline collocation methods for solving fractional differential equations, J. Comput. Appl.Math., 235 (2011), 3502-3514. [4 ] A. Pedas and E. Tamme, Numerical solution of nonlinear fractional differential equations by spline collocation methods, J. Comput. Appl.Math., 255 (2014), 216-230.
STABILITY OF COLLOCATION METHODS FOR FRACTIONAL DIFFERENTIAL EQUATIONS
Angelamaria Cardone
;Dajana Conte;Beatrice Paternoster
2018-01-01
Abstract
Collocation methods for fractional differential equations have been introduced by Blank [1] and later on rigorously analyzed by Pedas and Tamme [3,4]. Recently Cardone, Conte and Paternoster [2] introduced two step collocation methods, which raise the order of convergence, by using additional information from the past, without increasing the computational cost. Here we study the stability of both classes of methods, in order to nd methods with unbounded stability regions. This is a joint work with D. CONTE and B. PATERNOSTER from UNIVERSITY OF SALERNO. [1 ] L. Blank, Numerical treatment of differential equations of fractional order, Nonlinear World, 4 (1997), 473-491. [2 ] A. Cardone, D. Conte, B. Paternoster, Two-step collocation methods forfractional dierential equations, to appear in Discrete Cont.Dyn.-B. [3 ] A. Pedas and E. Tamme, On the convergence of spline collocation methods for solving fractional differential equations, J. Comput. Appl.Math., 235 (2011), 3502-3514. [4 ] A. Pedas and E. Tamme, Numerical solution of nonlinear fractional differential equations by spline collocation methods, J. Comput. Appl.Math., 255 (2014), 216-230.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
