Numerical solution of sixth-order boundary-value problems using Legendre wavelet collocation method

Numerical solution of sixth-order boundary-value problems using Legendre wavelet collocation method

An efficient method is proposed to approximate sixth order boundary value problems. The proposed method is based on Legendre wavelet in which Legendre polynomial is used. The mechanism of the method is to use collocation points that converts the differential equation into a system of algebraic equat...

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Main Authors: Muhammad Sohaib, Sirajul Haq, Safyan Mukhtar, Imad Khan
Format: Article
Language:English
Published: Elsevier 2018-03-01
Series:Results in Physics
Online Access:http://www.sciencedirect.com/science/article/pii/S2211379717323392
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spelling doaj-412a9dfa647e498a8e8576cd0f7dc0772020-11-24T23:54:18ZengElsevierResults in Physics2211-37972018-03-01812041208Numerical solution of sixth-order boundary-value problems using Legendre wavelet collocation methodMuhammad Sohaib0Sirajul Haq1Safyan Mukhtar2Imad Khan3Department of Mathematics and Statistics, Bacha Khan University, Charsadda 24461, Pakistan; Corresponding author.Faculty of Engineering Sciences, GIK Institute, Topi 23640, KPK, PakistanDepartment of Mathematics and Statistics, Bacha Khan University, Charsadda 24461, PakistanDepartment of Mathematics and Statistics, Bacha Khan University, Charsadda 24461, Pakistan; Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, PakistanAn efficient method is proposed to approximate sixth order boundary value problems. The proposed method is based on Legendre wavelet in which Legendre polynomial is used. The mechanism of the method is to use collocation points that converts the differential equation into a system of algebraic equations. For validation two test problems are discussed. The results obtained from proposed method are quite accurate, also close to exact solution, and other different methods. The proposed method is computationally more effective and leads to more accurate results as compared to other methods from literature. Keywords: Wavelet, Legendre polynomial, Legendre wavelet collocation method, Sixth order boundary value problemshttp://www.sciencedirect.com/science/article/pii/S2211379717323392
collection DOAJ
language English
format Article
sources DOAJ
author Muhammad Sohaib
Sirajul Haq
Safyan Mukhtar
Imad Khan
spellingShingle Muhammad Sohaib
Sirajul Haq
Safyan Mukhtar
Imad Khan
Numerical solution of sixth-order boundary-value problems using Legendre wavelet collocation method
Results in Physics
author_facet Muhammad Sohaib
Sirajul Haq
Safyan Mukhtar
Imad Khan
author_sort Muhammad Sohaib
title Numerical solution of sixth-order boundary-value problems using Legendre wavelet collocation method
title_short Numerical solution of sixth-order boundary-value problems using Legendre wavelet collocation method
title_full Numerical solution of sixth-order boundary-value problems using Legendre wavelet collocation method
title_fullStr Numerical solution of sixth-order boundary-value problems using Legendre wavelet collocation method
title_full_unstemmed Numerical solution of sixth-order boundary-value problems using Legendre wavelet collocation method
title_sort numerical solution of sixth-order boundary-value problems using legendre wavelet collocation method
publisher Elsevier
series Results in Physics
issn 2211-3797
publishDate 2018-03-01
description An efficient method is proposed to approximate sixth order boundary value problems. The proposed method is based on Legendre wavelet in which Legendre polynomial is used. The mechanism of the method is to use collocation points that converts the differential equation into a system of algebraic equations. For validation two test problems are discussed. The results obtained from proposed method are quite accurate, also close to exact solution, and other different methods. The proposed method is computationally more effective and leads to more accurate results as compared to other methods from literature. Keywords: Wavelet, Legendre polynomial, Legendre wavelet collocation method, Sixth order boundary value problems
url http://www.sciencedirect.com/science/article/pii/S2211379717323392
work_keys_str_mv AT muhammadsohaib numericalsolutionofsixthorderboundaryvalueproblemsusinglegendrewaveletcollocationmethod
AT sirajulhaq numericalsolutionofsixthorderboundaryvalueproblemsusinglegendrewaveletcollocationmethod
AT safyanmukhtar numericalsolutionofsixthorderboundaryvalueproblemsusinglegendrewaveletcollocationmethod
AT imadkhan numericalsolutionofsixthorderboundaryvalueproblemsusinglegendrewaveletcollocationmethod
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