| 线性非齐次方程待定函数法及相关定理证明 |
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| 引用本文： | 夏志. 线性非齐次方程待定函数法及相关定理证明[J]. 辽宁工程技术大学学报(自然科学版), 2006, 25(4): 638-640 |
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| 作者姓名： | 夏志 |
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| 作者单位： | 渤海大学,数学系,辽宁,锦州,121000 |
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| 基金项目： | 辽宁省教育厅资助项目(2004C057) |
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| 摘 要： | 把数理方程混合问题的方程和边界条件视为一个整体，给出了齐次方程加齐次边界条件的形式通解的概念并证明了相关定理，还证明了非齐次方程加非齐次边界条件的形式通解的结构定理，总结了待定函数法解题步骤及一般形式，提供了求解线性非齐次方程混合问题的简便解法。
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| 关 键 词： | 形式通解 分离变量法 待定函数法 |
| 文章编号： | 1008-0562(2006)04-0638-03 |
| 修稿时间： | 2005-09-12 |
Theorem of method of undetermined function for linear nonhomogeneous and its proof |
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| XIA Zhi. Theorem of method of undetermined function for linear nonhomogeneous and its proof[J]. Journal of Liaoning Technical University (Natural Science Edition), 2006, 25(4): 638-640 |
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| Authors: | XIA Zhi |
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| Abstract: | In this paper,regarding the boundary condition of the mixed problem of equation of mathematical physics as a unity,we present the concept of formal general solution of homogeneous equation with homogeneous boundary condition and the proof of relevant theorem.Furthermore,we prove the structure theorem of general solution of nonhomogeneous equation with nonhomogenous boundary condition.Finally,we list the steps of method of undetermined function and its applicable range,This paper provides a simple method for solving the mixed problem of linear nonhomogeneous equation. |
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| Keywords: | formal general solution method of separation of variables method of undetermined function |
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