Solving the forward-backward heat equation with a non-overlapping domain decomposition method based on multiquadric RBF meshfree 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 subproblems‎, ‎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 finite 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 efficient in comparison with the previous works‎.