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

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 L 2 stable. The existence and uniqueness of the numerical solution are discussed in detail. The convergence study gives the approximation orders under L 2 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. [ABSTRACT FROM AUTHOR]