In the article, we study the approximate numerical solution to the boundary value problem in ordinary diïŹerential equations. In the present article, a third-order two-point boundary value problem is considered for discussion. We developed a second order accurate ïŹnite diïŹerence method for the approximate numerical solution of the considered problem. We took a special boundary condition; we did not ïŹnd this boundary condition in the literature. We have discussed the standard convergence analysis of the proposed method. Numerical experiments on linear, nonlinear, and obstacle problems approve the order of accuracy and eïŹciency of the method.