三维泊松方程基于Richardson外推法的高阶紧致差分方法  

A High-Order Compact Difference Method Based on Richardson Extrapolation for the 3D Poisson Equation

作　　者：马月珍[1,2] 葛永斌[1] 王燕[1] 

机构地区：[1]宁夏大学数学计算机学院,宁夏银川750021 [2]宁夏同心县回民中学,宁夏同心751300

出　　处：《数学的实践与认识》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)

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.

关 键 词：三维泊松方程 高阶紧致差分方法 RICHARDSON外推法 交替方向隐式迭代 

分 类 号：O241.82[理学—计算数学]