Computational Method For Determining An Unknown Heat Source In Heat Equation

In this paper, the method of fundamental solutions(MFS) is used to deter-mine an unknown heat source term in a heat equation from overspecified boundary measurement data. The MFS is an inherently meshless technique for solving par-tial differential equations and the basic idea is to approximate the solution of the problem by a linear combination of fundamental solutions for the governing differential equation. By a function transformation, the inverse source problem is changed into an inverse initial data problem. Since the matrix arising from the MFS discretization is severely ill-conditioned, the standard Tikhonov regular-ization 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 five numerical examples in one-dimensional and two-dimensional cases.