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修正的Bakhvalov-Shishkin网格上奇异摄动问题的一致收敛性 被引量:2

Uniform convergence analysis of a singular perturbation problem on a modified Bakhvalov-Shishkin mesh
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摘要 研究具有两个边界层的奇异摄动两点边界值问题,为了提高其数值解的精度,构造了修正的Bakhvalov-Shishkin网格及相应的离散差分格式,并且利用Green函数证明了该差分格式具有O(N-2),一致于摄动参数ε的收敛阶,从而本质上改进了在Shishkin网格上得到的结果,即相应的差分格式具有关于ε一致的收敛阶O(N-2ln2N),其中N为网格结点数.最后用数值例子说明该方法的可行性. A numerical method based on a finite difference scheme with a modified BakhvalovShishkin mesh is given for the singularly perturbed twopoint boundary value problems. The scheme derived is convergent uniformly with respect to the perturbation parameter ε, which shows that the modified BakhvalovShishkin mesh is superior to the Shishkin mesh. The convergence order is improved to O(N-2) from O(N-2ln-2N), where N is the point numbers of the meshes. The proof is based on the Green function. The numerical example is given to underline the theoretical results.
机构地区 浙江大学数学系
出处 《浙江大学学报(理学版)》 CAS CSCD 2003年第3期263-267,共5页 Journal of Zhejiang University(Science Edition)
基金 国家自然科学基金资助项目(10271112) 浙江省自然科学基金资助项目(204019).
关键词 奇异摄动两点边界值问题 数值解 Bakhvalov-Shishkin网格 离散差分格式 一致收敛性 singular perturbation difference scheme modified Bakhvalov-Shishkin mesh uniform convergence
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参考文献11

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共引文献6

同被引文献9

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