Multilevel anti-derivative wavelets with augmentation for nonlinear boundary value problems
Somlak Utudee, Montri Maleewong · Advances in Difference Equations · 2017
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 $2^{s}$ , $0\leq s\leq p$ when p is the order of the Daubechies wavelets. Various examples of the Dirichlet boundary conditions are shown to confirm the theoretical results.