@article{Liu2011PolynomialSA, title={Polynomial spline approach for solving second-order boundary-value problems with Neumann conditions}, author={Li-Bin Liu and Huan-Wen Liu and Yanping Chen}, journal={Applied Mathematics and Computation}, year={2011}, volume={217}, pages={6872-6882} }

- Published 2011 in Applied Mathematics and Computation
DOI:10.1016/j.amc.2011.01.047

In this paper, a new difference scheme based on quartic splines is derived for solving linear and nonlinear second-order ordinary differential equations subject to Neumann-type boundary conditions. The scheme can achieve sixth order accuracy at the interior nodal points and fourth order accuracy at and near the boundary, which is superior to the well-known Numerov’s scheme with the accuracy being fourth order. Convergence analysis of the present method for linear cases is discussed. Finally… CONTINUE READING

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