Reconstructing unknown nonlinear boundary conditions in a time-fractional inverse reaction-diffusion-convection problem

摘要

This paper has focused on unknown functions identification in nonlinear boundary conditions of an inverse problem of a time-fractional reaction-diffusion-convection equation. This inverse problem is generally ill-posed in the sense of stability, that is, the solution of problem does not depend continuously on the input data. Thus, a combination of the mollification regularization method with Gauss kernel and a finite difference marching scheme will be introduced to solve this problem. The generalized cross-validation choice rule is applied to find a suitable regularization parameter. The stability and convergence of the numerical method are investigated. Finally, two numerical examples are provided to test the effectiveness and validity of the proposed approach.