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.