Numerical Algorithms

, Volume 59, Issue 2, pp 249–269 | Cite as

An improved non-local boundary value problem method for a cauchy problem of the Laplace equation

Original Paper


In this paper, we propose an improved non-local boundary value problem method to solve a Cauchy problem for the Laplace equation. It is known that the Cauchy problem for the Laplace equation is severely ill-posed, i.e., the solution does not depend continuously on the given Cauchy data. Convergence estimates for the regularized solutions are obtained under a-priori bound assumptions for the exact solution. Some numerical results are given to show the effectiveness of the proposed method.


Ill-posed problem Cauchy problem Laplace equation Regularization method Convergence estimate 


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© Springer Science+Business Media, LLC. 2011

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsLanzhou UniversityLanzhou CityPeople’s Republic of China
  2. 2.Department of MathematicsHexi UniversityZhangye CityPeople’s Republic of China

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