中文摘要：

基于Richardson外推法提出了一种求解二维和三维波动方程的高阶紧致差分方法．该方法首先利用四阶紧致交替方向隐式（ADI）差分格式，其截断误差为0（τ2＋h4），在不同尺寸的网格上对原方程进行求解，然后利用Richardson外推技术外推一次，得到了二维和三维波动方程具有O（τ4＋h6）精度的数值解，数值实验验证了该方法的高阶精度及有效性．

英文摘要：

A high - order compact difference method based on the Richardson extrapolation technique was proposed to solve the two - and three - dimensional wave equations. For a particular implementation, firstly, numerical results were obtained on different size meshes by using a high order alternating direction implicit （ADI） difference scheme, which was of order 0 （τ2 ＋ h4 ）. Then, the Richardson extrapolation method was used to get an 0 （ τ4 ＋ h6 ） accuracy solution for the two - and - three - dimensional problems. The numerical experiments are given to demonstrate the high accuracy and validity of the present method.