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Pitfalls in fast numerical solvers for fractional differential equations. (English) Zbl 1078.65550
Summary: We consider the problem of implementing fast algorithms for the numerical solution of initial value problems of the form \(x^{(\alpha)}(t)=f(t,x(t)), x(0)=x_{0}\), where \(x^{(\alpha)}\) is the derivative of \(x\) of order \(\alpha\) in the sense of Caputo and \(0<\alpha < 1\). We review some of the existing methods and explain their respective strengths and weaknesses. We identify and discuss potential problems in the development of generally applicable schemes.

MSC:
65L05 Numerical methods for initial value problems involving ordinary differential equations
Software:
FracPECE
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