We apply a radial basis function (RBF) meshless method to the one dimensional forward-backward heat equation. The physical domain is divided into two subdomains resulting in two standard forward and backward subproblems. An RBF meshfree method is applied to each subproblem assuming a virtual bundary between the subdomains and using an initial approximate solution on the interface. A finite difference scheme is employed for the time derivative and an iterative domain decomposition method is used to achieve a desired accuracy. Some numerical results will be given to show the effectiveness of the new method
