An O(h 6 ) numerical solution of general nonlinear fifth-order two point boundary value problems

@article{Rashidinia2010AnO6,
title={An O(h 6 ) numerical solution of general nonlinear fifth-order two point boundary value problems},
author={Jalil Rashidinia and Mohammad Ghasemi and R. Jalilian},
journal={Numerical Algorithms},
year={2010},
volume={55},
pages={403-428}
}

A sixth-order numerical scheme is developed for general nonlinear fifth-order two point boundary-value problems. The standard sextic spline for the solution of fifth order two point boundary-value problems gives only O(h 2) accuracy and leads to non-optimal approximations. In order to derive higher orders of accuracy, high order perturbations of the problem are generated and applied to construct the numerical algorithm. O(h 6) global error estimates obtained for these problems. The convergenceâ€¦Â CONTINUE READING