西南师范大学学报（自然科学版）
西南師範大學學報（自然科學版）
서남사범대학학보（자연과학판）
JOURNAL OF SOUTHWEST CHINA NORMAL UNIVERSITY
2013年
12期
50-54
,共5页
二维热传导方程%ADI方法%高精度紧致格式%Richardson外推法
二維熱傳導方程%ADI方法%高精度緊緻格式%Richardson外推法
이유열전도방정%ADI방법%고정도긴치격식%Richardson외추법
two-dimensional heat equation%ADI method%high-order compact scheme%Richardson extrap-olation method
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 Richard-son 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。
基于 Richardson 外推法提齣瞭一種數值求解二維熱傳導方程的高階緊緻差分方法。該方法首先利用時間二階、空間四階精度的緊緻交替方嚮隱式(ADI)差分格式在不同呎吋的網格上對原方程進行求解，然後利用 Richard-son 外推技術外推一次，最終得到瞭二維熱傳導方程時間四階、空間六階精度的數值解，數值實驗驗證瞭該方法的高階精度及有效性。
기우 Richardson 외추법제출료일충수치구해이유열전도방정적고계긴치차분방법。해방법수선이용시간이계、공간사계정도적긴치교체방향은식(ADI)차분격식재불동척촌적망격상대원방정진행구해，연후이용 Richard-son 외추기술외추일차，최종득도료이유열전도방정시간사계、공간륙계정도적수치해，수치실험험증료해방법적고계정도급유효성。
A high-order compact difference method,which is based on the Richardson extrapolation tech-nique,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 accu-rate in time and sixth order accurate in space.The numerical results are given to demonstrate the high ac-curacy and effectiveness of the present method.
