中文摘要：

首先对双曲型方程作Laplace变换得到椭圆型方程,再使用四阶高精度的差分格式并行地求解5个椭圆型差分方程.在求得椭圆型差分方程的近似解后,用Zakian反演法得到双曲型方程在任何时刻的高精度数值解;数值实验表明了此方法十分地有效.

英文摘要：

By means of Laplace transformation the hyperbolic differential equations are transformed to the elliptic differential equations which can be solved by the fourth order finite difference equations in parallel.After getting the approximate solutions of the elliptic differential equations,we can achieve the numerical solutions with high accruracy in any time for the hyperbolic differential equations by using the Zakian inversion method.At last,we carry out one numerical experiment to indicate that the method in this paper is very effective.