| 抛物型方程非齐次边值问题的推广型LOD有限差分及有限元格式 |
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| 引用本文： | 王彩华,王同科. 抛物型方程非齐次边值问题的推广型LOD有限差分及有限元格式[J]. 高等学校计算数学学报, 2006, 28(2): 138-150 |
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| 作者姓名： | 王彩华 王同科 |
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| 作者单位： | 天津师范大学数学科学学院,天津,300384 |
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| 基金项目： | 国家自然科学基金项目(10471079)资助． |
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| 摘 要： | 1引言本文考虑区域Ω=[0,1]~d(d=2,3)上的非齐次抛物型方程第一边值问题(?)-C_1△u C_2u=f(x,t),x∈Ω,t∈(0,T],(1．1) u(x,0)=u_0(x),x∈Ω,(1．2) u(x,t)=(?)(x,t),x∈(?)Ω,t∈(0,T],(1．3)其中C_1,C_2为常数且C_1＞0,C_2≥0．对于以上问题,可以使用有限差分方法及有限元方法进行离散,并采用交替方向方法求解．交替方向方法能够将高维问题转化为一系列的一维问题进行计算,具有计算量少,计算稳定且易于并行实现等优点,在大规模科学计算中起着非常重要的作用,一直是计算数
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| 关 键 词： | 非齐次边值问题 抛物型方程 有限元格式 有限差分 LOD 第一边值问题 |
| 收稿时间： | 2004-03-01 |
| 修稿时间： | 2004-03-01 |
EXTENDED LOCALLY ONE-DIMENSIONAL FINITE DIFFERENCE AND FINITE ELEMENT SCHEMES FOR NONHOMOGENEOUS PARABOLIC DIFFERENTIAL EQUATIONS WITH NONHOMOGENEOUS BOUNDARY CONDITIONS |
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| Wang Caihua,Wang Tongke. EXTENDED LOCALLY ONE-DIMENSIONAL FINITE DIFFERENCE AND FINITE ELEMENT SCHEMES FOR NONHOMOGENEOUS PARABOLIC DIFFERENTIAL EQUATIONS WITH NONHOMOGENEOUS BOUNDARY CONDITIONS[J]. Numerical Mathematics A Journal of Chinese Universities, 2006, 28(2): 138-150 |
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| Authors: | Wang Caihua Wang Tongke |
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| Affiliation: | School of Mathematical Science, Tianjin Normal University, Tianjin 300384 |
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| Abstract: | This paper presents some extended locally one-dimensional finite dif- ference and finite element schemes for nonhomogeneous parabolic differential equa- tions with nonhomogeneous boundary conditions.It is proved that these finite difference schemes have second order accuracy with respect to discrete L~2 norm. Finally,the schemes are illustrated by numerical examples and the results are very satisfactory. |
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| Keywords: | two and three dimensional parabolic differential equation nonhomogenerous boundary condition finite difference scheme finite element method extended locally one-dimensioanl scheme error estimate. |
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