Mean value methods for solving the heat equation backwards in time
Numerical Analysis
2020-12-01 v1 Numerical Analysis
Abstract
We investigate an iterative mean value method for the inverse (and highly ill-posed) problem of solving the heat equation backwards in time. Semi-group theory is used to rewrite the solution of the inverse problem as the solution of a fixed point equation for an affine operator, with linear part satisfying special functional analytical properties. We give a convergence proof for the method and obtain convergence rates for the residual. Convergence rates for the iterates are also obtained under the so called source conditions.
Keywords
Cite
@article{arxiv.2011.14685,
title = {Mean value methods for solving the heat equation backwards in time},
author = {A. Leitao},
journal= {arXiv preprint arXiv:2011.14685},
year = {2020}
}
Comments
13 pages. arXiv admin note: text overlap with arXiv:2011.08629