Based on the two dimensions elastic wave
equation with the Hamiltonian system, an eighth-order NAD-SPRK algorithm is obtained by combining the NAD
operator for higher order partial derivatives of discrete space and the
symplectic partitioned Runge-Kutta algorithm of discrete time derivative. The
stability conditions, numerical dispersion and computational efficiency of the algorithm
are studied theoretically and numerically. The results show that compared with
the fourth-order NSPRK algorithm, the eighth-order Lax-Wendroff algorithm and the eighth-order
staggered grid algorithm, the eighth-order NAD-SPRK algorithm is significantly superior to
the traditional numerical algorithm in suppressing the numerical dispersion, and has the minimum numerical
error and the highest computational efficiency.