000225936 001__ 225936
000225936 005__ 20190317000637.0
000225936 0247_ $$2doi$$a10.1007/s10915-015-0089-1
000225936 022__ $$a0885-7474
000225936 02470 $$2ISI$$a000391930500015
000225936 037__ $$aARTICLE
000225936 245__ $$aHigh-Order Accurate Local Schemes for Fractional Differential Equations
000225936 260__ $$bSpringer Verlag$$c2017$$aNew York
000225936 269__ $$a2017
000225936 300__ $$a31
000225936 336__ $$aJournal Articles
000225936 520__ $$aHigh-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.
000225936 6531_ $$aFractional differential equations
000225936 6531_ $$aVolterra equations
000225936 6531_ $$aHigh-order methods
000225936 700__ $$0247596$$g239799$$aBaffet, Daniel
000225936 700__ $$aHesthaven, Jan S.$$g232231$$0247428
000225936 773__ $$j70$$tJournal Of Scientific Computing$$k1$$q355-385
000225936 8564_ $$uhttps://infoscience.epfl.ch/record/225936/files/hoAccLocalSchemesFDEs_1.pdf$$zPreprint$$s879745$$yPreprint
000225936 909C0 $$xU12703$$0252492$$pMCSS
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000225936 917Z8 $$x232231
000225936 917Z8 $$x232231
000225936 937__ $$aEPFL-ARTICLE-225936
000225936 973__ $$rREVIEWED$$sPUBLISHED$$aEPFL
000225936 980__ $$aARTICLE