A multiscale Runge-Kutta Galerkin method for one-dimensional sine-Gordon equations
Jian Chen · Applied Mathematical Sciences · 2014
In this paper the multiscale Runge-Kutta Galerkin method is presented for solving sine-Gordon equations. The multiscale Galerkin method based on the multiscale orthonormal bases constructed in [8] is used to discrete the spacial variable, and the classical four order explicit RungeKutta method is applied to solve the resulting nonlinear ordinary differential equations. Because of the strong expression of the multiscale bases and the stability of the Runge-Kutta method, stable and accurate approximate solutions are obtained in relatively low dimensional subspaces. All numerical results illustrate the effectiveness of the proposed algorithm. Mathematics Subject Classification: 65J15; 65M60