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Journal of Scientific Computing

, Volume 70, Issue 1, pp 355–385 | Cite as

High-Order Accurate Local Schemes for Fractional Differential Equations

  • Daniel BaffetEmail author
  • Jan S. Hesthaven
Article

Abstract

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 \(L^2\) space. To obtain the schemes this expansion is terminated after \(P+1\) 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.

Keywords

Fractional differential equations Volterra equations High-order methods 

Notes

Acknowledgments

This work was partially supported by the NSF DMS-1115416 and by OSD/AFOSRFA9550-09-1-0613.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.MATHICSEÉcole Polytechnique Fédérale de Lausanne (EPFL)LausanneSwitzerland

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