Fractional Adams–Moulton methods

Luciano Galeone and Roberto Garrappa

Mathematics and Computers in Simulation (MATCOM), 2008, vol. 79, issue 4, 1358-1367

Abstract: In the simulation of dynamical systems exhibiting an ultraslow decay, differential equations of fractional order have been successfully proposed. In this paper we consider the problem of numerically solving fractional differential equations by means of a generalization of k-step Adams–Moulton multistep methods. Our investigation is focused on stability properties and we determine intervals for the fractional order for which methods are at least A(π/2)-stable. Moreover we prove the A-stable character of k-step methods for k=0 and k=1.

Keywords: Fractional differential equation; Multistep method; Adams–Moulton; Convergence; Stability (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:79:y:2008:i:4:p:1358-1367

DOI: 10.1016/j.matcom.2008.03.008

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