Higher-order finite-difference methods for nonlinear second-order two-point boundary-value problems Original Research Article

Finite-difference methods of orders six and eight are presented for second-order, non-linear, boundary-value problems. Both methods are economical in the sense that they use few function evaluations at interior grid points. The implementation of the methods is straightforward. The convergence of the methods is discussed. Numerical examples are considered to demonstrate computationally their order of convergence.