Fast multilevel augmentation methods for nonlinear boundary value problems

We develop a multilevel augmentation method for solving nonlinear boundary value problems. We first describe the multilevel augmentation method for solving nonlinear operator equations of the second kind which has been proposed in our recent paper Chen et al. (2011) [16], and then apply it to solving the nonlinear two-point boundary value problems of second-order differential equations. The theoretical analysis of convergence order and computational complexity are proposed. Finally numerical experiments are presented to confirm the theoretical estimates and illustrate the efficiency of the method.