Fully Discrete Discontinuous Galerkin Method Based On Differential Transformation Strategy

Based on the differential transform strategy,we introduce high order full discrete discontinuous Galerkin methods for one-dimensional hyperbolic conservation laws.Compared with the standard discontinuous Galerkin methods,the current methods enjoy the following advantages including low storage as well as keeping arbitrary high order accuracy in time.In comparison with the ADER methods,the resulting methods avoid the complicated Cauchy-Kowalewski procedure and the coding is easy at the same time.In addition,numerical results also indicate that the resulting methods enjoy genuine high order accuracy for smooth solutions and keep steep discontinuity transition at the same time.