In this paper, a difference scheme based on the quartic splines for solving the singularly-perturbed two-point boundary-value problem of second-order ordinary differential equations subject to Neumann-tpye boundary conditions are derived. The accuracy order of the schemes is O(h~4) not only at the interior nodal points but also at the two endpoints, which are better than general center finite difference method. Finally, the numerical results are given to illustrate the efficiency of our methods.
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