The extrapolation of Numerov's scheme for nonlinear two-point boundary value problems

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

“…However, the accuracies of most previous numerical results are of second order only and the highest accuracy is of fourth order [10]. In addition, although much work has been done to solve the problem subject to Dirichlet boundary conditions, very little literature pay attention to the case of Neumann boundary conditions.…”

“…This fact makes numerical solutions of considerable practical interest and there are many numerical 0096-3003/$ -see front matter Ó 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2011.01.047 techniques available including several well-known methods, such as finite difference methods [6][7][8], Numerov method [9][10][11][12], spline method [13][14][15][16][17], shooting method [18,19].…”

Numerov′s Method for a Class of Nonlinear Multipoint Boundary Value Problems

“…Although many theoretical investigations have focused on Numerov's method for two-point boundary conditions such as 1.1 d cf. 40,41,43,44,[47][48][49][50][51] , there is relatively little discussion on the analysis of Numerov's method applied to fully multipoint boundary conditions in 1.1 . The study presented in this paper is aimed at filling in such a gap by considering Numerov's method for the numerical solution of the multipoint boundary value problem 1.1 with the more general boundary conditions, including the boundary conditions 1.1 a , 1.1 b , and 1.1 c .…”