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首页> 外文期刊>Journal of inverse and ill-posed problems >A quasi-boundary-value method for the Cauchy problem for elliptic equations with nonhomogeneous Neumann data
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A quasi-boundary-value method for the Cauchy problem for elliptic equations with nonhomogeneous Neumann data

机译：具有非齐次Neumann数据的椭圆型方程的柯西问题的拟边界值方法

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摘要

A Cauchy problem for elliptic equations with nonhomogeneous Neumann data in a cylindrical domain is investigated in this paper. For the theoretical aspect the a-priori and a-posteriori parameter choice rules are suggested and the corresponding error estimates are obtained. About the numerical aspect, for a simple case results given by two methods based on the discrete Sine transform and the finite difference method are presented; an idea of left-preconditioned GMRES (Generalized Minimum Residual) method is proposed to deal with the high dimensional case to save the time; a view of dealing with a general domain is suggested. Some ill-posed problems regularized by the quasi-boundary-value method are listed and some rules of this method are suggested.
机译：研究了圆柱域中具有非齐次Neumann数据的椭圆方程的柯西问题。对于理论方面，提出了先验参数和后验参数选择规则，并获得了相应的误差估计。关于数值方面，对于简单情况，提出了两种基于离散Sine变换和有限差分法的结果。提出了一种左预处理GMRES（广义最小残差）方法来处理高维情况以节省时间。建议处理通用领域。列出了通过拟边界值法正则化的一些不适定问题，并提出了该方法的一些规则。

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