Numerical solution of nonlinear three-point boundary value problem on the positive half-line

In this paper, we present an efficient numerical algorithm to solve the three-point boundary value problem on the half-line based on the reproducing kernel theorem. Considering the boundary conditions including a limit form, a new weighted reproducing kernel space is established to overcome the difficulty. By applying reproducing property and existence of the orthogonal basis in the weighted reproducing kernel space, the approximate solution is constructed by the orthogonal projection of the exact solution. Convergence has also been discussed. We demonstrate the accuracy of the method by numerical experiments.