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

摘要

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.