A numerical method based on the polynomial regression for the inverse diffusion problem
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, cilt.92, sa.9, ss.1883-1894, 2015 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 92 Sayı: 9
- Basım Tarihi: 2015
- Doi Numarası: 10.1080/00207160.2014.884712
- Dergi Adı: INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.1883-1894
- Kocaeli Üniversitesi Adresli: Evet
Özet
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.