High-Order Accurate Local Schemes for Fractional Differential Equations

High-order methods inspired by the multi-step Adams methods are proposed for systems of fractional differential equations. The schemes are based on an expansion in a weighted space. To obtain the schemes this expansion is terminated after terms. We study the local truncation error and its behavior with respect to the step-size h and P. Building on this analysis, we develop an error indicator based on the Milne device. Methods with fixed and variable step-size are tested numerically on a number of problems, including problems with known solutions, and a fractional version on the Van der Pol equation.


Published in:
Journal Of Scientific Computing, 70, 1, 355-385
Year:
2017
Publisher:
New York, Springer Verlag
ISSN:
0885-7474
Keywords:
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 Record created 2017-02-17, last modified 2019-03-17

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