Pitfalls in fast numerical solvers for fractional differential equations

Authors:
Kai Diethelm;Judith M. Ford;Neville J. Ford;Marc Weilbeer
Affiliations:
GNS Gesellschaft für Numerische Simulation mbH, Braunschweig, Germany and Institut für Angewandte Mathematik, Technische Universität Braunschweig, Braunschweig, Germany;Royal Liverpool Children's NHS Trust, Liverpool, UK and Department of Mathematics, UMIST, Manchester, UK;Department of Mathematics, University College Chester, Chester, UK;Institut für Angewandte Mathematik, Technische Universität Braunschweig, 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(α)(t) = f(t, x(t)), x(0) = x0, where x(α) is the derivative of x of order α in the sense of Caputo and 0