Finite di_erence method for numerical solution of two point boundary value problems with non-uniform mesh and internal boundary condition

الملخص EN

In this article, we have presented a variable step nite di erence method for solving second order boundary value problems in ordinary di erential 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 con rm the theoretical conclusions of the proposed method.

The computational results obtained for these model problems suggest that method is ecient and accurate.