Solving Nonlinear Boundary Value Problems Using the Higher Order Haar Wavelet Method

Abstract

The current study is focused on development and adaption of the higher order Haar wavelet method for solving nonlinear ordinary differential equations. The proposed approach is implemented on two sample problems—the Riccati and the Liénard equations. The convergence and accuracy of the proposed higher order Haar wavelet method are compared with the widely used Haar wavelet method. The comparison of numerical results with exact solutions is performed. The complexity issues of the higher order Haar wavelet method are discussed.

Keywords

• numerical methods
• Haar wavelet method
• higher order wavelet expansion
• numerical rate of convergence
• nonlinear equations
• quasilinearization