| 最小二乘法求解非线性四阶边值问题 |
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| 引用本文： | 贺亮,吕学琴. 最小二乘法求解非线性四阶边值问题[J]. 哈尔滨师范大学自然科学学报, 2011, 27(2): 4-8 |
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| 作者姓名： | 贺亮 吕学琴 |
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| 作者单位： | 哈尔滨师范大学 |
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| 基金项目： | 国家自然科学基金项目(61071181);哈尔滨师范大学青年学术骨干资助计划项目(10KXQ-05);黑龙江省青年科学基金(QC2010036) |
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| 摘 要： | 在再生核空间中构造了一种新的算法,研究了一类带有非线性边值问题的数值求解算法.该文基于再生核理论结合最小二乘法来求解四阶非线性边值问题,该理论是基于再生核空间W52[0,1],方程的精确解以级数的形式在再生核空间W52[0,1]中给出,同时给出了一些算例说明了这个方法的有效性.
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| 关 键 词： | 非线性四阶边值问题 再生核空间 最小二乘法 |
Least Square Method to Solve Nonlinear Fourth-order Boundary Value Problem |
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| He Liang , Lv Xueqin. Least Square Method to Solve Nonlinear Fourth-order Boundary Value Problem[J]. Natural Science Journal of Harbin Normal University, 2011, 27(2): 4-8 |
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| Authors: | He Liang Lv Xueqin |
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| Affiliation: | (Harbin Normal University) |
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| Abstract: | In this paper,a new algorithm is studied for a class of boundary value problems with nonlinear numerical algorithm based on renewable nuclear.Combining theory with least square method to solve four order nonlinear boundary value problems,and based on renewable nuclear space W52,the exact solution of the equation in the form of series in renewable nuclear space W52 is given.And some numerical examples show the effectiveness of the proposed method. |
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| Keywords: | Linear fourth-order boundary value problems Regeneration nuclear space Least squares |
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