The numerical solution of a nonlocal boundary value problem for an ordinary second-order differential equation by the finite difference method

In the article a numerical technique based on the finite difference method is proposed for the approximate solution of a second order nonlocal boundary value problem for ordinary differential equations. It is clear that a bridge designed with two support points at each end point leads to a standard two-point local boundary value condition, and a bridge contrived with multi-point supports corresponds to a multi-point boundary value condition. At the same time if non-local boundary conditions can be set up near each endpoint of a multi-point support bridge, a two-point nonlocal boundary condition arises. The computational results for the nonlinear model problem are presented to validate the proposed idea. The effect of parameters variation on the convergence of the proposed method is analyzed.