4.1 Convergence of the algorithm
We use Figure1 to illustrate the time convergence of the numerical algorithm. The result indicates that the algorithm we propose in this paper has the fourth-order convergence rate in time because the logarithmic-logarithmic graph is parallel to the fourth-order convergence slope, while the Crank-Nicolson time-stepped finite element method has the second-order convergence rate. High-order discretization of space and time means that the algorithm has higher accuracy than second-order discretization under the same number of time steps and space nodes.