Numerical algorithm based on an implicit fully discrete local discontinuous Galerkin method for the time-fractional KdV-Burgers-Kuramoto equation
This provides a stable and accurate numerical scheme for solving a complex fractional partial differential equation, which is of interest to researchers in computational mathematics and applied sciences.
The authors developed a fully discrete local discontinuous Galerkin method for the time-fractional KdV-Burgers-Kuramoto equation, proving unconditional stability and L2 error estimates with convergence rate O(h^{k+1}+(Δt)^2+(Δt)^{α/2}h^{k+1/2}). Numerical examples demonstrate efficiency and accuracy.
In this paper, a 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 $O(h^{k+1}+(Δt)^2+(Δt)^\fracα{2}h^{k+1/2})$. Numerical examples are presented to show the efficiency and accuracy of our scheme.