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新疆大学数学系!新疆乌鲁木齐830046,新疆大学数学系!新疆乌鲁木齐830046,新疆大学数学系,新疆,乌鲁木齐,830046
Published:2000
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[1]冯新龙,王焕焕,阿不都热西提.求解一维热传导方程数值解的高精度方法[J].新疆大学学报(自然科学版),2000(03):13-18.
冯新龙, 王焕焕, 阿不都热西提. 求解一维热传导方程数值解的高精度方法[J]. Journal of Xinjiang University (Natural Science Edition in Chinese and English), 2000, (3).
[1]冯新龙,王焕焕,阿不都热西提.求解一维热传导方程数值解的高精度方法[J].新疆大学学报(自然科学版),2000(03):13-18. DOI:
冯新龙, 王焕焕, 阿不都热西提. 求解一维热传导方程数值解的高精度方法[J]. Journal of Xinjiang University (Natural Science Edition in Chinese and English), 2000, (3). DOI:
利用加权隐格式
在固定网比的前提下
得到修正加权因子θopt
利用此θopt求解一维热传导方程所得到的数值解
同 Crank- Nicholson格式求得的数值解相比
具有更高的精度
并在此基础上
在一定的加细划分下求解
同样得到了较好的高精度数值解
In this paper
we obtain the revised weighted factor \%θ\-\{opt\%\} by the weighted implicit scheme on the condition of invariable mesh ratio.Then
using the very \%θ\-\{opt\%\}
we solve one dimensional heat equation and get higher accuracy than the solution of \%Crank Nicholson\% scheme is.Finally
when using the same \%θ\-\{opt\%\} and denser mesh division
we can also get the highly accurate numerical solution which is relatively good.
[1 ] John Noye.Finite difference methods for partial differential equations[M] .South Australia:Universityof Adelaide,1 980 .
[2 ] Leon Lapidus,George F.Numerical solution of partial differential equations in science and engineering[M] .Princeton University:Pinder.1 982 .
徐长发 .实用偏微分方程数值解法 [M] .武汉 :华中理工大学出版社 ,1 990
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