Solving an inverse problem for a parabolic equation with a nonlocal boundary condition in the reproducing kernel space

On the basis of a reproducing kernel space, an iterative algorithm for solving the inverse problem for heat equation with a nonlocal boundary condition is presented. The analytical solution in the reproducing kernel space is shown in a series form and the approximate solution vn is constructed by truncating the series to n terms. The convergence of vn to the analytical solution is also proved. Results obtained by the proposed method imply that it can be considered as a simple and accurate method for solving such inverse problems.