Abstract
AbstractWe investigate the numerical treatment of fractional derivatives using a discontinuous Galerkin approach. We consider fractional differential equations in one dimension.The most common definitions, the Riemann‐Liouville and Caputo derivatives, as well as a third definition are considered. Different types of initial condition statements are investigated for the extended discontinuous Galerkin method.We obtain numerical results on the order of convergence in the L2 and H1 norms. We compare the classical discontinuous Galerkin method with our adapted approach and show results for the different types of fractional derivatives.Further work was carried out on parabolic differential equations with fractional time derivatives, which is to be published cf. [2]. A keystone in the further research is the development of analytical tools for theoretical convergence results. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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