Homotopy analysis method for discrete quasi-reversibility mollification method of nonhomogeneous backward heat conduction problem

Abstract

In this article, the inverse time problem is investigated. Regarding the ill-posed linear problem, utilize the quasi-reversibility method first. This problem has been regularized and after that provides an iterative regularizing strategy for noisy input data that are based on homotopy. For the regularizing solution, the error analysis is proved when we employ noisy measurement data as our initial guess. Finally, numerical implementations are presented.

Keywords

• heat conduction
• backward conduction
• ill-posed problem
• homotopy analysis method
• quasi-reversibility
• discrete mollification