Numerical analysis for distributed-order differential equations

In this paper we present and analyse a numerical method for the solution of a distributed-order differential equation of the general form ∫ 0 m A ( r , D ∗ r u ( t ) ) d r = f ( t ) where m is a positive real number and where the derivative D ∗ r is taken to be a fractional derivative of Caputo type...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2009-03, Vol.225 (1), p.96-104
Main Authors: Diethelm, Kai, Ford, Neville J.
Format: Article
Language:English
Subjects:
Convergence
Distributed-order differential equation
Exact sciences and technology
Global analysis, analysis on manifolds
Mathematical analysis
Mathematics
Multi-term fractional differential equation
Numerical analysis
Numerical analysis. Scientific computation
Numerical solution
Ordinary differential equations
Real functions
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Summary:In this paper we present and analyse a numerical method for the solution of a distributed-order differential equation of the general form ∫ 0 m A ( r , D ∗ r u ( t ) ) d r = f ( t ) where m is a positive real number and where the derivative D ∗ r is taken to be a fractional derivative of Caputo type of order r . We give a convergence theory for our method and conclude with some numerical examples.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2008.07.018