Abstract
We present an extrapolation type algorithm for the numerical solution of fractional order differential equations. It is based on the new result that the sequence of approximate solutions of these equations, computed by means of a recently published algorithm by Diethelm [6], possesses an asymptotic expansion with respect to the stepsize. From this we conclude that the application of extrapolation is justified, and we obtain a very efficient differential equation solver with practically no additional numerical costs. This is also illustrated by a number of numerical examples.
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Diethelm, K., Walz, G. Numerical solution of fractional order differential equations by extrapolation. Numerical Algorithms 16, 231–253 (1997). https://doi.org/10.1023/A:1019147432240
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DOI: https://doi.org/10.1023/A:1019147432240