Multilevel anti-derivative wavelets with augmentation for nonlinear boundary value problems

Abstract

© 2017, The Author(s). The multilevel augmentation method with the anti-derivatives of the Daubechies wavelets is presented for solving nonlinear two-point boundary value problems. The anti-derivatives of the Daubechies wavelets are applied as the multilevel bases for the subspaces of approximate solutions. This process results in a full nonlinear system that can be solved by the multilevel augmentation method for reducing computational cost. The convergence rate of the present method is shown. It is the order of 2s, 0 ≤ s≤ p when p is the order of the Daubechies wavelets. Various examples of the Dirichlet boundary conditions are shown to confirm the theoretical results.