中文摘要：

为快速求解Sine-Gordon方程,提出了一种紧致差分格式和龙格-库塔方法相结合的方法。数值实验表明,相较于Sine-Gordon方程的真解,该方法是有效的,且精度高、误差小。

英文摘要：

In order to solve Sine-Gordon equation rapidly,a method based on the compact finite difference scheme and the diagonally implicit Runge-Kutta（DIRKN）method is proposed.The solution of the method is high accuracy and the error estimate is small.The numerical experiments show that the method is effective.