| 一类具有混合边界条件的半有界弦振动初值问题求解方法 |
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| 引用本文： | 张琳.一类具有混合边界条件的半有界弦振动初值问题求解方法[J].新乡学院学报(自然科学版),2012(2):105-106,109. |
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| 作者姓名： | 张琳 |
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| 作者单位： | 陕西理工学院数学与计算机科学学院,陕西汉中723001 |
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| 摘 要： | 研究了一类具有混合边界条件的半有界弦振动初值问题的求解方法，对初始位移函数ψ（x）和初始速度函数ψ（x）做适当延拓，给出了满足延拓函数条件的公式，并利用达朗贝尔公式对该问题求解．对于类似的非齐次方程问题，可先将非齐次方程转化为齐次方程，然后借助本方法求解．
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| 关 键 词： | 弦振动方程初值问题 混合边界 达朗贝尔公式 |
Method for Solving a Class of Initial Value Problemsof Semi-bounded String Vibrating with Mixed Boundary Condition |
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| Authors: | ZHANG Lin |
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| Institution: | ZHANG Lin (College of Mathematics and Computer Science, Shanxi University of Technology, Hanzhong 723001, China) |
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| Abstract: | A method is discussed for solving a class of initial value problems with mixed boundary condition of semi-bounded vibrating strings. And proper prolongation of the initial displacement function ψ（x） and the initial velocity function ψ（x） are given. The formula satisfying the prolongations is provided and solution is obtained from D＇Alembert formula. The equation can be converted into homogeneous one, and then solved with the equation for the similar problems of nonhomogeneous equations. |
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| Keywords: | initial problem of vibrating-string equations mixed boundary condition D＇Alembert formula |
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