The discontinuous Galerkin finite element approximation of the multi-order fractional initial problems

Yunying Zheng, Zhengang Zhao and Yanfen Cui

Applied Mathematics and Computation, 2019, vol. 348, issue C, 257-269

Abstract: In this paper, we construct a discontinuous Galerkin finite element scheme for the multi-order fractional ordinary differential equation. The analysis of the stability shows the scheme is L2 stable. The existence and uniqueness of the numerical solution are discussed in detail. The convergence study gives the approximation orders under L2 norm and L∞ norm. Numerical examples demonstrate the effectiveness of the theoretical results. The oscillation phenomena are also found during numerical tracing a non-linear multi-order fractional initial problem.

Keywords: Multi-order fractional differential equation; Caputo derivative; Galerkin finite element method; Discontinuous Galerkin finite element method; Stability (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:348:y:2019:i:c:p:257-269

DOI: 10.1016/j.amc.2018.11.057

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