Numerical algorithm based on an implicit fully discrete local discontinuous Galerkin method for the time-fractional KdV-Burgers-Kuramoto equation

摘要

In this paper, an implicit fully discrete local discontinuous Galerkin (LDG) finite element method is considered for solving the time-fractional KdV-Burgers-Kuramoto (KBK) equation. The scheme is based on a finite difference method in time and local discontinuous Galerkin methods in space. We prove that our scheme is unconditional stable and L~2 error estimate for the linear case with the convergence rate O(h~(k+1) + (Δ t)~2+ (Δ t)~(α/2)h~(k+)12). Numerical examples are presented to show the efficiency and accuracy of our scheme.