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

• Main Authors: Somlak Utudee, Montri Maleewong
• Format: Journal
• Published: 2018
• Subjects: Agricultural and Biological Sciences; Arts and Humanities
• Online Access: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85017020981&origin=inward; http://cmuir.cmu.ac.th/jspui/handle/6653943832/46993
• Institution: Chiang Mai University

© 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 2 s , 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.