高维波动方程基于Richardson外推法的高阶紧致差分方法  

High-order Compact Difference Method Based on Richardson Extrapolation for the High Dimensional Wave Equation

作　　者：徐丽[1] 马月珍[2] 葛永斌[2] 

机构地区：[1]宁夏师范学院数学计算机科学学院,宁夏固原756000 [2]宁夏大学数学计算机学院,宁夏银川750021

出　　处：《绍兴文理学院学报》2011年第10期1-6,共6页Journal of Shaoxing University

基　　金：国家自然科学基金资助项目(11061025);教育部科学技术研究重点项目(210239);霍英东教育基金会高等院校青年教师基金资助项目(121105);宁夏自然科学基金资助项目(NZ10230)

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O(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.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.

关 键 词：高维波动方程 高阶紧致格式 交替方向隐式方法 RICHARDSON外推法 

分 类 号：O241.82[理学—计算数学]