Approximation of backward heat conduction problem using Gaussian radial basis functions

In this work an efficient numerical method is applied for investigation of the backward heat conduction problem in an unbounded region. The problem is ill-posed, in the sense that the solution if it exists, does not depend continuously on the data. The Gaussian radial basis functions are used for discretization of the problem. The presented method is reducing the problem to an interpolation problem which is more simple than the collocation type method. To regularize the resultant ill-conditioned linear system of equations, we apply successfully both the Tikhonov regularization technique and the L-curve method to obtain a stable numerical approximation to the solution. A new convenient and simply applicable method is derived. The stability and convergence of the proposed method are investigated. Two examples are presented to illustrate efficiency and accuracy of the proposed method.