A meshless method for solving an inverse spacewise-dependent heat source problem

In this paper an effective meshless and integration-free numerical scheme for solving an inverse spacewise-dependent heat source problem is proposed. Due to the use of the fundamental solution as basis functions, the method leads to a global approximation scheme in both spatial and time domains. The standard Tikhonov regularization technique with the generalized cross-validation criterion for choosing the regularization parameter is adopted for solving the resulting ill-conditioned system of linear algebraic equations. The effectiveness of the algorithm is illustrated by several numerical examples.