A novel meshless method in conjunction with a regularization technique for solving the transient heat source with additive noise

Abstract

We consider the problem of determination to ill-conditioned heat sources in unsteady 2-D heat conduction problems. The method we consider is truly mesh-free and is particularly suited to the inverse problem and is called the backward substitution method (BSM). We derive that when this method is coupled with the Crank–Nicholson (CN) discretizations of time and Tikhonov regularization, one demonstrates the proposed method is easy to implement and pretty accurate at an appropriate parameter concerning noise in the data. Also, a trigonometric basis function (TBF) that enforces approximate interpolation on boundary conditions yields an ill-conditional matrix. Finally, we assess the feasibility of the proposed method by numerical simulations and experiments.