摘要
提出了数值求解二维抛物型方程的一种新的高精度加权平均紧致隐格式 ,利用Fourier分析方法证明了该格式是无条件稳定的 .为了克服传统迭代法在求解隐格式时收敛速度慢的缺陷 ,利用了多重网格加速技术 ,大大加快了迭代收敛速度 ,提高了求解效率 .
A new high order compact weighted average implicit difference scheme for the two dimensional (2 D) Parabolic equation is presented and proved unconditional stable by Fourier analysis.A multigrid method is employed to overcome the difficulties when traditional relaxation methods are used to treat the implicit difference schemes.Numerical experiments are conducted to compare the new scheme with the existing schemes and the multigrid algorithms with the traditional relaxation method.It is shown that the new scheme is computationally more accurate than the second order schemes and multigrid algorithms are more efficient than the traditional relaxation method.
出处
《应用数学》
CSCD
北大核心
2003年第2期13-18,共6页
Mathematica Applicata
基金
国家自然科学基金资助项目 (1970 2 0 0 8)
宁夏自然科学基金资助项目
