In this article, we have presented a variable step ﬁnite diﬀerence method for solving second order boundary value problems in ordinary diﬀerential equations with an internal boundary condition. We have discussed the convergence and established at least cubic order of accuracy of the proposed method. The proposed method tested on several model problems for the numerical solution. The numerical results obtained for these model problems with known / constructed exact solution conﬁrm the theoretical conclusions of the proposed method. The computational results obtained for these model problems suggest that method is eﬃcient and accurate.
free text keywords: Boundary Value Problem, Convergence of the Method, Cubic Order, Finite Difference Method, Variable Step., lcsh:Mathematics, lcsh:QA1-939