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The numerical solution of fractional differential equations: speed versus accuracy. (English) Zbl 0976.65062

This paper is concerned with the numerical solution of fractional differential equations where the fraction derivatives are understood in the so-called Caputo version [cf. M. Caputo, Linear models of dissipation whose \(Q\) is almost frequency independent II, Geophys. J. Roy. Astronom. Soc. 13, 529-539 (1967)]. Since the definition of the fractional derivative requires a convolution integral and numerical methods must approximate in some way this integral the main drawback of numerical methods for this type of equations is that they are computationally expensive.
In this paper the authors propose some techniques for reducing the amount of computational effort to solve some fractional differential equations studying their effect on the error of the approximate solutions.

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
26A33 Fractional derivatives and integrals
65L70 Error bounds for numerical methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations

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