Polynomial spline approach for solving second-order boundary-value problems with Neumann conditions

@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}
}
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