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| 摘要: |
| 本文研究了带非齐次Dirichlet及Neumann数据的一类Helmholtz型方程柯西问题. 该问题是不适定的，需要利用正则化方法恢复其数值稳定性。文章首先在解的先验假设下建立问题的条件稳定性，然后利用修正Lavrentiev正则化方法克服其不适定性，并结合正则化参数的先验与后验选取规则获得了正则化解的Holder收敛性结果. 相应的数值实验结果验证了所提方法是稳定可行的. |
| 关键词: 不适定问题 柯西问题 Helmholtz型方程 修正 Lavrentiev正则化方法 收敛性估计 |
| DOI： |
| 分类号:O175.25; O175.29 |
| 基金项目:国家自然科学基金项目；宁夏自然科学基金项目 |
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| Modified Lavrentiev regularization method for the Cauchy problem of Helmholtz-type equation |
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张宏武
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| Abstract: |
| In this paper, a Cauchy problem of Helmholtz-type equation with nonhomogeneous Dirichlet and Neumann datum is investigated, this problem is highly ill-posed and some regularization techniques are needed to be imposed to restore the numerical stability. We establish the result of conditional stability under an a-priori assumption for exact solution. A modified Lavrentiev method is constructed to deal with this problem, and under an a-priori and an a-posteriori selection rule for the regularization parameter, the convergence estimate of Holder type for this method is derived. The corresponding numerical experiments are done to verify that our regularization method is stable and workable. |
| Key words: Ill-posed problem Cauchy problem Helmholtz-type equation Modified Lavrentiev method Convergence estimate |
