中文摘要：

采用截断误差修正方法,改进了3维泊松方程的传统中心差分格式.首先通过限制算子估算出了粗网格上的截断误差,然后结合插值算子,将其还原到细网格上,修正原差分方程,得到了具有4阶精度的新格式.该方法不但继承了传统中心差分格式计算板型简单的优点,而且具有较高的精度,是一种提高低阶格式精度的新方法.最后通过数值实验,验证了该方法的精确性和优越性.

英文摘要：

The truncation error correction method is used to improve the accuracy of the traditional central difference scheme for the 3D Poisson equation.Firstly the truncation error on the coarse grid is estimated by the restriction operator.Then combing with the interpolation operator,the error to the fine grid is restored and the original difference equation is corrected.A new fourth order scheme is derived.The new method inherits the advantage of the central difference scheme,improves its accuracy order and provides a new way to turn a low order scheme into a high order scheme.Numerical experiments for the problems demonstrate the accuracy and superiority of the present method.