CAJ | 학술논문

本文研究了三维热传导方程的紧交替方向隐式差分格式.利用算子方法导出了紧交替方向隐式差分格式,并利用Fourier分析方法证明了差分格式的收敛性和绝对稳定性,Richardson外推法外推一次得到具有O(T3+h6)阶精度的近似解.本文方法是对二维热传导方程问题的推广,同样适用于多维的情形.
본문연구료삼유열전도방정적긴교체방향은식차분격식.이용산자방법도출료긴교체방향은식차분격식,병이용Fourier분석방법증명료차분격식적수렴성화절대은정성,Richardson외추법외추일차득도구유O(T3+h6)계정도적근사해.본문방법시대이유열전도방정문제적추엄,동양괄용우다유적정형.
An efficient high order compact alternating direction implicit (ADI) method is developed for solving three-dimensional heat equations by introducing some differential operators.It is shown by the discrete Fourier analysis that this new ADI scheme is unconditionally stable and the truncation error O(T-3 + h6) is also gained with once Richardson's extrapolation. The method can be generalized to the multi-dimensional case.