| 具有一阶转向点的大参数二阶线性微分方程解的高次逼近与误差估计 |
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| 引用本文： | 时红廷,杜江. 具有一阶转向点的大参数二阶线性微分方程解的高次逼近与误差估计[J]. 华中科技大学学报(城市科学版), 1994, 0(2) |
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| 作者姓名： | 时红廷 杜江 |
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| 作者单位： | 首都师范大学，江汉石油学院 |
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| 摘 要： | 本文运用Ｇｒｏｎｗａｌｌ－Ｂｅｌｌｍａｎ不等式及其变形并结合Ａｉｒｙ函数的性质讨论了具有一个一阶转向点的合大参数ｕ的二阶线性微分方程的解的高次逼近及其误差估计．使用的方法不同于以前其他作者处理同类问题时所用的方法。本文不仅得到了Ｏｌｖｅｒ曾经得到的结果，而且给出两点新的结论．
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| 关 键 词： | 转向点，Airy函数，高次逼近，误差估计 |
The Higher Approximation and Error Estimate of the Solution of Second Order Linear Differential Equation with a Large Parameter and a Simple Turning Point |
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| Shi Hongting. The Higher Approximation and Error Estimate of the Solution of Second Order Linear Differential Equation with a Large Parameter and a Simple Turning Point[J]. Journal of Huazhong University of Science and Technology, 1994, 0(2) |
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| Authors: | Shi Hongting |
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| Abstract: | This poper studies the higher approximation and error estimates of the solutions of second order linearordinary differential equationWith a large paraxneter u and a simple turning POint by means of a variant of the Gronwall-Bellmaninequality and the properties of Airy functions.The method used in this paper is different from that in previous articles which discussed the similarproblems. We obtain not only Olver's results,but also two new ones. |
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| Keywords: | turning point Airy function higher approximation error estimate |
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