Numerical approximation of time-fractional Burgers-type equation

Abstract

In this work, we analyze and test a local discontinuous Galerkin method for solving the Burgers-type equation. The proposed numerical method, which is high-order accurate, is based on a finite difference scheme in time and local discontinuous Galerkin methods in space. We prove that the scheme is unconditionally stable and convergent. Some numerical tests are provided to illustrate the accuracy and capability of the scheme.