求解二维热传导方程的高精度紧致差分方法  

On a High-Order Compact Difference Method for Solving the Two-Dimensional Heat Equation

作　　者：魏剑英[1] 

机构地区：[1]宁夏大学数学计算机学院,银川750021

出　　处：《西南师范大学学报（自然科学版）》2013年第12期50-54,共5页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11061025;11361045);霍英东教育基金会高等院校青年教师基金(121105)

摘　　要：基于Richardson外推法提出了一种数值求解二维热传导方程的高阶紧致差分方法.该方法首先利用时间二阶、空间四阶精度的紧致交替方向隐式(ADI)差分格式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,最终得到了二维热传导方程时间四阶、空间六阶精度的数值解,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,which is based on the Richardson extrapolation technique,has been proposed to solve the two-dimensional heat equation.Firstly,numerical results have been obtained on different-size meshes by means of a high order alternating direction implicit（ADI）difference scheme,which is second order accurate in time and fourth order accurate in space.Then,the Richardson extrapolation method has been employed to compute a more accurate solution,which is fourth order accurate in time and sixth order accurate in space.The numerical results are given to demonstrate the high accuracy and effectiveness of the present method.

关 键 词：二维热传导方程 ADI方法 高精度紧致格式 RICHARDSON外推法 

分 类 号：O241.82[理学—计算数学]