Determination of an unknown heat flux and a spacewise dependent heat source in an IHCP by MFS

In this article, we will study the application of the method of fundamental solutions (MFS) for solving an inverse heat conduction problem (IHCP). The approximation of the heat flux at x = 0 and heat source that is space-dependent is considered. A transformation is used to simplify the problem. Then the unknowns are determined by MFS and Tikhonov regularization method with the generalized cross validation method (GCV). Finally, a numerical example is prepared to illustrate the accuracy of the present method.