| 自适应迎风格式求解奇异摄动两点边值问题的高精度算法(二) |
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| 引用本文： | 杨继明,陈艳萍. 自适应迎风格式求解奇异摄动两点边值问题的高精度算法(二)[J]. 高等学校计算数学学报, 2009, 31(3) |
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| 作者姓名： | 杨继明 陈艳萍 |
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| 作者单位： | 1. 湖南工程学院理学院,湘潭,411104
2. 华南师范大学数学科学学院,广州,510631 |
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| 基金项目： | 国家自然科学基金项目 10671163，湖南省教育厅科研资助项目07C219、06A069，湖南工程学院科研启动基金项目0854 |
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| 摘 要： | 0引言 考虑与文[1]相同的奇异摄动两点边值问题的数值解法: Tu(x):=-εu″(x)-p(x)u′(x)=f(x),x∈(0,1); (1) u(0)=0,u(1)=1. (2) 其中ε是一个常数,0<ε≤1,f∈C2[0,1].假定P∈C3[0,1]且存在常数β和-β使得0<β≤p(x)≤-β,|p′(x)|≤-β,(V)x∈[0,1] (3) 成立.
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| 关 键 词： | 求解 自适应 迎风格式 两点边值问题 数值解 一致收敛 奇异摄动 高精度算法 |
AN EFFICIENT ADAPTIVE ALGORITHM BASED ON UPWIND DIFFERENCE FOR A SINGULARLY PERTURBED TWO-POINT BOUNDARY VALUE PROBLEM |
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| Yang Jiming,Chen Yanping. AN EFFICIENT ADAPTIVE ALGORITHM BASED ON UPWIND DIFFERENCE FOR A SINGULARLY PERTURBED TWO-POINT BOUNDARY VALUE PROBLEM[J]. Numerical Mathematics A Journal of Chinese Universities, 2009, 31(3) |
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| Authors: | Yang Jiming Chen Yanping |
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| Affiliation: | Yang Jiming (College of Science,Hunan Institute of Engineering,Xiangtan 411104) Chen Yanping (School of Mathematical Science,South China Normal University,Guangzhou 510631) |
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| Abstract: | For a kind of singularly perturbed two-point boundary value problems in computational fluid dynamics,standard upwind difference operator is applied. An adaptive numerical solution algorithm using equidistribution principle is given based on Richardson extrapolation method.Theoretical analysis and some numerical results are presented to validate that the algorithm is feasible and efficient. |
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| Keywords: | singular perturbation upwind difference scheme adaptive mesh |
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