Reconstructing the Absorption Function in a Quasi-Linear Sorption Dynamic Model via an Iterative Regularizing Algorithm

Abstract

This study addresses the parameter identification problem in a system of time-dependent quasi-linear partial differential equations (PDEs). Using the integral equation method, we prove the uniqueness of the inverse problem in nonlinear PDEs. Moreover, using the method of successive approximations, we develop a novel iterative algorithm to estimate sorption isotherms. The stability results of the algorithm are proven under both a priori and a posteriori stopping rules. A numerical example is given to show the efficiency and robustness of the proposed new approach.

Existence of Fuzzy Fixed Points and Common Fuzzy Fixed Points for FG-Contractions with Applications

“…Zhane et al [3] obtained the non-negative stable approximate solutions to ill-posed linear operator equations in a Hilbert space setting which are based on fixed-point iterations in combination with preconditioning ideas. In [4], Shcheglov et al used the method of successive approximations to develop a novel iterative algorithm to estimate sorption isotherms.…”