| 二阶线性双曲型方程变换为常微分方程求解定理及应用 |
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| 引用本文： | 刘许成. 二阶线性双曲型方程变换为常微分方程求解定理及应用[J]. 大学数学, 2012, 28(1): 132-136. DOI: 10.3969/j.issn.1672-1454.2012.01.027 |
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| 作者姓名： | 刘许成 |
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| 作者单位： | 潍坊学院数学与信息科学学院,山东潍坊,261061 |
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| 摘 要： | 二个自变量的二阶线性双曲型方程auxx＋2buxy＋cuyy＋dux＋euy＋g=0,当系数a,b,c,d,e,g满足一定条件时,可以利用变换T：ξ=φ（x,y）,η=ψ（x,y）化为一阶线性常微分方程求解,本文给出了求解定理和计算方法.
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| 关 键 词： | 二阶线性双曲型方程 特征线 特征方程 |
The Solving Theorem that Second Order Linear Hyperbolic Equation Can Be Changed into Ordinary Differential Equation and Its Application |
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| LIU Xu-cheng. The Solving Theorem that Second Order Linear Hyperbolic Equation Can Be Changed into Ordinary Differential Equation and Its Application[J]. College Mathematics, 2012, 28(1): 132-136. DOI: 10.3969/j.issn.1672-1454.2012.01.027 |
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| Authors: | LIU Xu-cheng |
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| Affiliation: | LIU Xu-cheng(Department of Mathematics,Weifang University,Weifang,Shandong,261061,China) |
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| Abstract: | To the second order linear hyperbolic equation with two independent variables auxx+2buxy+cuyy+dux+euy+g=0 when its coefficients a,b,c,d,e satisfy given conditions,we may utilize the transformation T:ξ=φ(x,y),η=ψ(x,y) to make it as first order linear ordinary differential equation for solving.At the same time,we give the discrimination theorem and application method. |
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| Keywords: | second order linear hyperbolic equation eigenline eigenequation |
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