An efficient approximation method for the nonhomogeneous backward heat conduction problems

Jin Wen, Xiufen Cheng

This paper presents a new improved meshless numerical scheme to solve the nonhomogeneous backward heat conduction problems. Fundamental solutions of heat equations and radial basis functions of both   and   are employed to obtain a numerical  ill-conditioned, the Tikhonov regularization method is adopted to solve the resulting system of linear equations. Therefore, generalized cross-validation (GCV) method is used to choose a regularization parameter. The accuracy and efficiency of our proposed method is illustrated by several typical 1-D and 2-D numerical examples.