Efficient Numerical Scheme for the Solution of Tenth Order Boundary Value Problems by the Haar Wavelet Method

Rohul Amin, Kamal Shah, Imran Khan, Muhammad Asif, Mehdi Salimi and Ali Ahmadian
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Rohul Amin: Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtunkhwa 25120, Pakistan
Kamal Shah: Department of Mathematics, University of Malakand, Dir(L), Khyber Pakhtunkhwa 18000, Pakistan
Imran Khan: Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtunkhwa 25120, Pakistan
Muhammad Asif: Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtunkhwa 25120, Pakistan
Mehdi Salimi: Department of Mathematics & Statistics, McMaster University, Hamilton, ON L8S 4K1, Canada
Ali Ahmadian: Institute of IR 4.0, The National University of Malaysia (UKM), Bangi 43600, Malaysia

Mathematics, 2020, vol. 8, issue 11, 1-19

Abstract: In this paper, an accurate and fast algorithm is developed for the solution of tenth order boundary value problems. The Haar wavelet collocation method is applied to both linear and nonlinear boundary value problems. In this technqiue, the tenth order derivative in boundary value problem is approximated using Haar functions and the process of integration is used to obtain the expression of lower order derivatives and approximate solution for the unknown function. Three linear and two nonlinear examples are taken from literature for checking validation and the convergence of the proposed technique. The maximum absolute and root mean square errors are compared with the exact solution at different collocation and Gauss points. The experimental rate of convergence using different number of collocation points is also calculated, which is nearly equal to 2.

Keywords: boundary value problems; Gauss elimination method; collocation method; Haar wavelet (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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