| 求解椭圆方程柯西问题的修正吉洪诺夫正则化方法 |
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| 引用本文： | 谢瓯,赵振宇,孟泽红.求解椭圆方程柯西问题的修正吉洪诺夫正则化方法[J].应用数学与计算数学学报,2014,28(3):317-324. |
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| 作者姓名： | 谢瓯 赵振宇 孟泽红 |
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| 作者单位： | 1. 广东海洋大学理学院,广东湛江,520488
2. 浙江财经学院数学与统计学院,杭州,310018 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 研究了一类变系数椭圆方程的柯西问题,这类问题出现在很多实际问题领域.由于问题的不适定性,不可能通过经典的数值方法来求解上述问题,必须引入正则化手段.采用了一种修正吉洪诺夫正则化方法来求解上述问题.在一种先验和一种后验参数选取准则下,分别获得了问题的误差估计.数值例子进一步显示方法是稳定有效的.
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| 关 键 词： | 不适定问题 柯西问题 椭圆方程 吉洪诺夫正则化 偏差原理 误差估计 |
Solving Cauchy problem of elliptic equation by modified Tikhonov regularization method |
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| XIE Ou,ZHAO Zhen-yu,MENG Ze-hong.Solving Cauchy problem of elliptic equation by modified Tikhonov regularization method[J].Communication on Applied Mathematics and Computation,2014,28(3):317-324. |
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| Authors: | XIE Ou ZHAO Zhen-yu MENG Ze-hong |
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| Institution: | XIE Ou, ZHAO Zhen-yu, MENG Ze-hong (1. College of Science, Guangdong Ocean University, Zhanjiang 524088 Guangdong Province, China; 2. School of Mathematics and Statistics, Zhejing University of Finance and Economics, Hangzhou 310018, China) |
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| Abstract: | A Cauchy problem of an elliptic equation with variable coefficients is considered. This problem occurs in the study of many practical problems, and it is ill posed. Therefore, it is impossible to solve the problem using classical numerical methods and special techniques are required. A modified Tikhonov regularization method is presented, and the error estimates are obtained with a priori strategy and a posteriori choice rule to find the regularization parameter. Numerical tests show that the proposed method is effective and stable. |
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| Keywords: | ill-posed problem Cauchy problem elliptic equation Tikhonov reg-ularization method discrepancy principle error estimate |
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