数学杂志2017，Vol.37Issue(5)：1040-1046,7.
偏微分方程边值反问题的数值方法研究
NUMERICAL METHODS FOR SOLVING INVERSE BOUNDARY VALUE PROBLEM OF PARTIAL DIFFERENTIAL EQUATION
摘要
Abstract
In this paper, we study the application problem of singular integral equation in the inverse boundary value problem. Using the natural integral equation and its inversion formula on a circle, we transformed the Laplace equation inverse boundary value problem into a combination of a hypersingular integral equation and a weakly singular integral equation, then construct the corresponding collocation scheme based on the trigonometric interpolation, and use the Tikhonov regularization to solve the resulting linear equations. Numerical experiments show the effectiveness of the method.关键词
边值反问题/奇异积分方程/三角插值/Tikhonov正则化Key words
inverse boundary value problem/singular integral equation/trigonometric interpolation/Tikhonov regularization分类
数理科学引用本文复制引用
易苗,刘扬..偏微分方程边值反问题的数值方法研究[J].数学杂志,2017,37(5):1040-1046,7.基金项目
国家自然科学基金(11201358) （11201358）
中央高校基本科研业务费专项资金资助(2015IA007). （2015IA007）
