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

Abstract

AbstractIn 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 L2 error estimate for the linear case with the convergence rate O(hk+1 + (Δ t)2+ (Δ t)α/2hk+$^{1 \over 2}$). Numerical examples are presented to show the efficiency and accuracy of our scheme.