A numerical method based on the polynomial regression for the inverse diffusion problem


Erdem A.

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, vol.92, no.9, pp.1883-1894, 2015 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 92 Issue: 9
  • Publication Date: 2015
  • Doi Number: 10.1080/00207160.2014.884712
  • Title of Journal : INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
  • Page Numbers: pp.1883-1894

Abstract

In this paper we study two inverse problems relating to reconstruction of the diffusion coefficient k(x), appearing in a linear partial parabolic equation u(t)=(k(x)u(x))(x). One is concerned through overposed data u(x, T) and the other is with non-local boundary condition . We derive relations for these inverse problems, which show between changes in k(x) and changes in overposed data or the non-local boundary condition. They make us to help to construct an approximate solution based on the polynomial regression. We analyse the error in the approximation. Finally, some numerical experiments are presented.