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A finite difference method for the very weak solution to a Cauchy problem for an elliptic equation.
- Source :
- Journal of Inverse & Ill-Posed Problems; Dec2018, Vol. 26 Issue 6, p835-857, 23p
- Publication Year :
- 2018
-
Abstract
- We introduce the concept of very weak solution to a Cauchy problem for elliptic equations. The Cauchy problem is regularized by a well-posed non-local boundary value problem whose solution is also understood in a very weak sense. A stable finite difference scheme is suggested for solving the non-local boundary value problem and then applied to stabilizing the Cauchy problem. Some numerical examples are presented for showing the efficiency of the method. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09280219
- Volume :
- 26
- Issue :
- 6
- Database :
- Complementary Index
- Journal :
- Journal of Inverse & Ill-Posed Problems
- Publication Type :
- Academic Journal
- Accession number :
- 133427627
- Full Text :
- https://doi.org/10.1515/jiip-2018-0060