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A MODIFIED TIKHONOV REGULARIZATION METHOD FOR THE CAUCHY PROBLEM OF LAPLACE EQUATION

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【Author】 Fan YANG;Chuli FU;Xiaoxiao LI;School of Science, Lanzhou University of Technology;School of Mathematics and Statistics, Lanzhou University;

【机构】 School of Science, Lanzhou University of Technology； School of Mathematics and Statistics, Lanzhou University；

【摘要】 In this paper,we consider the Cauchy problem for the Laplace equation,which is severely ill-posed in the sense that the solution does not depend continuously on the data.A modified Tikhonov regularization method is proposed to solve this problem.An error estimate for the a priori parameter choice between the exact solution and its regularized approximation is obtained.Moreover,an a posteriori parameter choice rule is proposed and a stable error estimate is also obtained.Numerical examples illustrate the validity and effectiveness of this method.更多还原

【Abstract】 In this paper,we consider the Cauchy problem for the Laplace equation,which is severely ill-posed in the sense that the solution does not depend continuously on the data.A modified Tikhonov regularization method is proposed to solve this problem.An error estimate for the a priori parameter choice between the exact solution and its regularized approximation is obtained.Moreover,an a posteriori parameter choice rule is proposed and a stable error estimate is also obtained.Numerical examples illustrate the validity and effectiveness of this method.更多还原

【关键词】 Cauchy problem for Laplace equation； ill-posed problem； a posteriori parameter choice； error estimate；
【Key words】 Cauchy problem for Laplace equation； ill-posed problem； a posteriori parameter choice； error estimate；

【基金】 supported by the National Natural Science Foundation of China(11171136;11261032);the Distinguished Young Scholars Fund of Lan Zhou University of Technology(Q201015);the basic scientific research business expenses of Gansu province college;the Natural Science Foundation of Gansu province(1310RJYA021)

【文献出处】 Acta Mathematica Scientia(English Series) ,数学物理学报(英文版) , 编辑部邮箱 ,2015年06期

【分类号】O175
【被引频次】2
【下载频次】33

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