Numerical solution for series sine-Gordon equations using variational method and finite element approximation

摘要

This paper investigates numerical solutions for several kinds of sine-Gordon equations using variational method and finite element approximation. For the case of one-dimension and continuous time, a semi-discrete algorithm is proposed using Gauss–Legendre quadrature and Runge–Kutta method. Furthermore, the convergence of the algorithm is proved. Finally, several numerical examples are implemented and some simulation results are presented to show the efficiency of the scheme.