四阶常微分方程奇异摄动问题的四阶精度差分方法
Fourth-Order Accurate Difference Method for the Singular Perturbation Problem
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摘要: 在本文中,我们利用特殊的非均匀网格上的Hermite差分格式来近似四阶常微分方程奇异摄动问题,并证明了其四阶精度的一致收敛性,且在文章的最后给出了其数值结果.
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关键词:
- 非均匀网格 /
- 网格生成函数 /
- Hermite差分格式 /
- 一致收敛性
Abstract: In this paper,the numerical solution of fourth-order ordinary differential equations is considered.To approximate the differential equation,the Hermitian scheme on a special nonequidistant mesh is used.The fourth order convergence uniform in the perturbation parameter is proved.The numerical result shows the pomtwise convergence,too.-
Key words:
- nonequidistant mesh /
- mesh generating function /
- Hermitian scheme /
- uniformly convergence
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