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

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.