| 微分连续正则化方法与一维声波方程系数反演问题求解 |
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| 引用本文： | 韩波,杨晓军.微分连续正则化方法与一维声波方程系数反演问题求解[J].高校应用数学学报(A辑),1994(4):351-360. |
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| 作者姓名： | 韩波 杨晓军 |
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| 作者单位： | 哈尔滨工业大学 |
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| 摘 要： | 本文将求解非线性方程组的微分连续法与求解不问题的Ｔｉｋｈｏｎｏｖ正则化方法结合起来，形成了兼有大范围收性与稳定性的“微分连续正则化方法”，给出了方法的收敛性分析，文中最后给出的关于一维波动方程反问题的计算实例表明了方法的有效性。
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| 关 键 词： | 微分连续法 反问题 波动方程 解 |
DIFFERENTIAL CONTINUATION-REGULARIZATION METHOD AND THE COEFFICIENT INVERSE PROBLEM OF ONE-DIMENSIONAL WAVE EQUATIONS |
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| Han Bo,Yang Xiaojun,Liu Jiaqi.DIFFERENTIAL CONTINUATION-REGULARIZATION METHOD AND THE COEFFICIENT INVERSE PROBLEM OF ONE-DIMENSIONAL WAVE EQUATIONS[J].Applied Mathematics A Journal of Chinese Universities,1994(4):351-360. |
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| Authors: | Han Bo Yang Xiaojun Liu Jiaqi |
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| Institution: | Harbin Institute of Technology |
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| Abstract: | In this paper,differential continuation method for solving nonlinear system of equations and Tikhonov's regularization method for solving linear ill-posed problems are combined into the differential continuation-regularization method which is widely convergent and stable.Some results about their convergence are obtained.The applicabilities of this method to solving the inverse problem of one-dimensional wave equations are demonstrated.It is shown by numerical simulations that our method is feasible and effective. |
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| Keywords: | Differential Continuation Method Regularization Method Inverse Problem of Differential Equations |
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