On some explicit Adams multistep methods for fractional differential equations

Authors:
Roberto Garrappa
Affiliations:
University of Bari, Department of Mathematics, Via E. Orabona n. 4, 70125 Bari, Italy
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 6
Cited 6

Discretized fractional calculus

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Pitfalls in fast numerical solvers for fractional differential equations

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Fast and Oblivious Convolution Quadrature

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Fractional Adams-Moulton methods

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Explicit methods for fractional differential equations and their stability properties

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Mixed spline function method for reaction-subdiffusion equations

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A family of Adams exponential integrators for fractional linear systems

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Original article: On some generalizations of the implicit Euler method for discontinuous fractional differential equations

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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.