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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
FracPECE
Full Text:
##### References:
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