| 两类高阶高次非线性差分方程的精确解 |
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| 引用本文： | 龚东山,牛富俊,邓伟华,谢维维. 两类高阶高次非线性差分方程的精确解[J]. 宁夏大学学报(自然科学版), 2011, 0(3): 213-216 |
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| 作者姓名： | 龚东山 牛富俊 邓伟华 谢维维 |
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| 作者单位： | 中国科学院寒区旱区环境与工程研究所冻土工程国家重点实验室;兰州大学数学与统计学院;中交第一公路勘察设计研究院寒区道路工程实验室; |
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| 基金项目： | 国家自然科学基金资助项目(41030741);国家自然科学基金对外交流与合作项目(4064042420072);国家自然科学基金资助项目(10801067) |
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| 摘 要： | 利用独立通解法(UGS)研究2类非线性差分方程的精确解,得到了一类非线性齐次差分方程的精确解,它由若干个独立通解共同构成,且独立通解的个数与差分方程的阶数n和方程的次数m的乘积mm无关；还得到了一类非线性非齐次差分方程的一组特解.
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| 关 键 词： | 非线性 高阶 高次 差分方程 精确解 独立通解 特解 |
Exact Solution of Two Kinds of High-order and High-degree Non-linear Difference Equations |
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| Gong Dongshan,,,Niu Fujun,Deng Weihua,Xie Weiwei. Exact Solution of Two Kinds of High-order and High-degree Non-linear Difference Equations[J]. Journal of Ningxia University(Natural Science Edition), 2011, 0(3): 213-216 |
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| Authors: | Gong Dongshan Niu Fujun Deng Weihua Xie Weiwei |
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| Affiliation: | Gong Dongshan1,2,3,Niu Fujun1,Deng Weihua2,Xie Weiwei2 (1.State Key Laboratory of Frozen Soil of Engineering,Cold and Arid Regions Environmental and Engineering Research Institute,Chinese Academy of Sciences,Lanzhou 730000,China,2.School of Mathematics and Statistics,Lanzhou University,3.Cold Regions Road Engineering Laboratory,The First Highway Survey and Design Institute,Ministry of Communications,Xi'an 710068,China) |
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| Abstract: | The paper shows the exact solution of two kinds of non-linear difference equations by using the undependent general solution method.The exact solution for a kind of non-linear homogenous difference equations is formed by some undependent general solutions whose number is independent of the product of order n and degree m in the difference equations.A set of special solutions for a kind of non-linear and non-homogeneous difference equations are also given. |
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| Keywords: | non-linear high-order high-degree difference equation exact solution undependent general solution special solution |
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