Initial data identification in advection–diffusion processes via a reversed fixed-point iteration method

Cosgun T., Sarı M.

Journal of Computational and Applied Mathematics, vol.425, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 425
  • Publication Date: 2023
  • Doi Number: 10.1016/j.cam.2023.115057
  • Journal Name: Journal of Computational and Applied Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Computer & Applied Sciences, INSPEC, MathSciNet, Metadex, zbMATH, DIALNET, Civil Engineering Abstracts
  • Keywords: Advection–diffusion equation, Initial data identification, Inverse problems, Reversed fixed-point iteration method
  • Yıldız Technical University Affiliated: Yes

Abstract

© 2023 Elsevier B.V.In the present study, a novel method called the reversed fixed-point iteration method (RFPIM) is applied to obtain numerical responses of the advection–diffusion mechanisms. Heretofore, the RFPIM has been employed to find out unstable equilibria of nonlinear mappings defined on Banach spaces. The current paper implements the method to recover the initial data from the final data. The method has been tested under measurements including different levels of noise such as 5%, 10%, 30%, 50%, and 100% in the final time data, and the results indicate that the present technique could be regarded as a powerful tool in handling such inverse problems.