| 带有小参数的抛物型方程的多过渡点差分格式 |
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| 引用本文： | 蔡新.带有小参数的抛物型方程的多过渡点差分格式[J].厦门大学学报(自然科学版),2006,45(3):311-314. |
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| 作者姓名： | 蔡新 |
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| 作者单位： | 厦门大学数学科学学院,福建,厦门,361005 |
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| 摘 要： | 讨论两类时间上带有小参数的抛物型方程,介绍了多过渡点的选取方法,依此法构造不等距差分格式并证明新的差分格式关于摄动参数是一阶一致收敛.多过渡点差分格式的收敛阶与Bakhvalov法相同,高于Shishkin网格法,但计算量比Bakhvalov法小得多,在实际应用中相当有效.
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| 关 键 词： | 抛物型方程 多过渡点 一致收敛 小参数 |
| 文章编号： | 0438-0479(2006)03-0311-04 |
| 收稿时间： | 07 15 2005 12:00AM |
| 修稿时间： | 2005年7月15日 |
Multi-transition Points Difference Schemes for Parabolic Problem with Small Parameter |
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| CAI Xin.Multi-transition Points Difference Schemes for Parabolic Problem with Small Parameter[J].Journal of Xiamen University(Natural Science),2006,45(3):311-314. |
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| Authors: | CAI Xin |
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| Institution: | School of Mathematical Science,Xiamen University,Xiamen 361005,China |
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| Abstract: | Two kinds of parabolic partial differential equation with a small parameter in time variable are considered.The technique of select multi-transition points is introduced.According to multi-transition points method,non-equidistant difference scheme is constructed.The new method is proved to be first-order uniform convergence with respect to the perturbed parameter.The rate of convergence is higher than Shishkin's scheme,while it is the same convergence accuracy as Bakhnvalov's.The computing work is more easier than Bakhnvalov's.The new method is useful in practice application. |
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| Keywords: | small parameter parabolic uniform convergence multi-transition points |
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