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

Mart Ratas, Jüri Majak and Andrus Salupere
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Mart Ratas: Deptartment of Cybernetics, School of Science, Tallinn University of Technology, 12616 Tallinn, Estonia
Jüri Majak: Deptartment of Mechanical and Industrial Engineering, School of Engineering, Tallinn University of Technology, 12616 Tallinn, Estonia
Andrus Salupere: Deptartment of Cybernetics, School of Science, Tallinn University of Technology, 12616 Tallinn, Estonia

Mathematics, 2021, vol. 9, issue 21, 1-12

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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