Solving the forward-backward heat equation with a non-overlapping domain decomposition method based on multiquadric RBF mesh- free method

In this paper, we present a numerical technique to deal with the one-dimensional forward-backward heat equations. First, the physical domain is divided into two non-overlapping subdomains resulting in two separate forward and backward sub- problems, and then a meshless method based on multiquadric radial basis functions is employed to treat the spatial variables in each subproblem using the Kansa's method. We use a time discretization scheme to approximate the time derivative by the forward and backward nite difference formulas. In order to have adequate boundary conditions for each subproblem, an initial approximate solution is assumed on the interface boundary, and the solution is improved by solving the subproblems in an iterative way. The numerical results show that the proposed method is very useful and computationally effcient in comparison with the previous works.