Pitfalls in fast numerical solvers for fractional differential equations

Authors:
Kai Diethelm;Judith M. Ford;Neville J. Ford;Marc Weilbeer
Affiliations:
Institut für Angewandte Mathematik, Technische Universität Braunschweig, Pockelsstraíe 14, 38106 Braunschweig, Germany;Department of Mathematics, UMIST, PO Box 88, Manchester M60 1QD,UK;Department of Mathematics, University College Chester, Parkgate Road, Chester CH1 4BJ, UK;Institut für Angewandte Mathematik, Technische Universität Braunschweig, Pockelsstraíe 14, 38106 Braunschweig, Germany
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

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Abstract

We consider the problem of implementing fast algorithms for the numerical solution of initial value problems of the form x^(^@a^)(t)=f(t,x(t)), x(0)=x"0, where x^(^@a^) is the derivative of x of order @a in the sense of Caputo and 0