摘要
基于Richardson外推法提出了数值求解三维泊松方程的高阶紧致差分方法.方法通过利用四阶和六阶紧致差分格式,分别在细网格和粗网格上求解,然后利用Richardson外推技术和算子插值方法,得到三维泊松方程在细网格上的六阶和八阶精度的数值解.数值实验结果验证了该方法的精确性和有效性.
A new high-order compact finite difference method based on the Richardson extrapolation technique is proposed to solve the three-dimensioned Poisson equation. For a particular implementation, a fine grid equation and a coarse grid equation are solved by using a fourth-order and sixth-order compact difference scheme, then the Richardson extrapolation and an operator interpolation scheme are used by combining the two approximate solutions to get a sixth-order and eighth-order accuracy solution on fine grid. Numerical experiments are conducted to verify the accuracy and effectiveness of present method.
出处
《数学的实践与认识》
CSCD
北大核心
2011年第8期146-152,共7页
Mathematics in Practice and Theory
基金
国家自然科学基金(10502026
10662006)
