In this paper we present a family of explicit formulas for the numerical solution of differential equations of fractional order. The proposed methods are obtained by modifying, in a suitable way, Fractional-Adams-Moulton methods and they represent a way for extending classical Adams-Bashforth multistep methods to the fractional case. The attention is hence focused on the investigation of stability properties. Intervals of stability for k-step methods, k = 1,...,5, are computed and plots of stability regions in the complex plane are presented. (C) 2008 Elsevier B.V. All rights reserved.
On some explicit Adams multistep methods for fractional differential equations
GARRAPPA, Roberto
2009-01-01
Abstract
In this paper we present a family of explicit formulas for the numerical solution of differential equations of fractional order. The proposed methods are obtained by modifying, in a suitable way, Fractional-Adams-Moulton methods and they represent a way for extending classical Adams-Bashforth multistep methods to the fractional case. The attention is hence focused on the investigation of stability properties. Intervals of stability for k-step methods, k = 1,...,5, are computed and plots of stability regions in the complex plane are presented. (C) 2008 Elsevier B.V. All rights reserved.File in questo prodotto:
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