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

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 high...

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Autores principales:	Mart Ratas, Jüri Majak, Andrus Salupere
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	numerical methods Haar wavelet method higher order wavelet expansion numerical rate of convergence nonlinear equations quasilinearization Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/facb58d4f57943dcae6581d0a0970904
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spelling	oai:doaj.org-article:facb58d4f57943dcae6581d0a09709042021-11-11T18:20:32ZSolving Nonlinear Boundary Value Problems Using the Higher Order Haar Wavelet Method10.3390/math92128092227-7390https://doaj.org/article/facb58d4f57943dcae6581d0a09709042021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2809https://doaj.org/toc/2227-7390The 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.Mart RatasJüri MajakAndrus SalupereMDPI AGarticlenumerical methodsHaar wavelet methodhigher order wavelet expansionnumerical rate of convergencenonlinear equationsquasilinearizationMathematicsQA1-939ENMathematics, Vol 9, Iss 2809, p 2809 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	numerical methods Haar wavelet method higher order wavelet expansion numerical rate of convergence nonlinear equations quasilinearization Mathematics QA1-939
spellingShingle	numerical methods Haar wavelet method higher order wavelet expansion numerical rate of convergence nonlinear equations quasilinearization Mathematics QA1-939 Mart Ratas Jüri Majak Andrus Salupere Solving Nonlinear Boundary Value Problems Using the Higher Order Haar Wavelet Method
description	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.
format	article
author	Mart Ratas Jüri Majak Andrus Salupere
author_facet	Mart Ratas Jüri Majak Andrus Salupere
author_sort	Mart Ratas
title	Solving Nonlinear Boundary Value Problems Using the Higher Order Haar Wavelet Method
title_short	Solving Nonlinear Boundary Value Problems Using the Higher Order Haar Wavelet Method
title_full	Solving Nonlinear Boundary Value Problems Using the Higher Order Haar Wavelet Method
title_fullStr	Solving Nonlinear Boundary Value Problems Using the Higher Order Haar Wavelet Method
title_full_unstemmed	Solving Nonlinear Boundary Value Problems Using the Higher Order Haar Wavelet Method
title_sort	solving nonlinear boundary value problems using the higher order haar wavelet method
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/facb58d4f57943dcae6581d0a0970904
work_keys_str_mv	AT martratas solvingnonlinearboundaryvalueproblemsusingthehigherorderhaarwaveletmethod AT jurimajak solvingnonlinearboundaryvalueproblemsusingthehigherorderhaarwaveletmethod AT andrussalupere solvingnonlinearboundaryvalueproblemsusingthehigherorderhaarwaveletmethod
_version_	1718431919763357696

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

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