Haar Wavelet Method for the Solution of Sixth-Order Boundary Value ProblemsSource: Journal of Computational and Nonlinear Dynamics:;2025:;volume( 020 ):;issue: 004::page 41004-1Author:Amin, Rohul
DOI: 10.1115/1.4067859Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: In this article, a numerical scheme is developed for the solution of sixth-order boundary value problems (BVP). The Haar collocation method is developed for both linear and nonlinear boundary value problems. In this method, the sixth-order derivative in boundary value problem is approximated using Haar functions, and integration is used to obtain the values of lower derivatives and approximate solution. Some examples are given for the convergence of the proposed method. The Haar technique devoted in this paper is compared with Septic spline method, Sine–Galerkin method, and decomposition method. Maximum absolute and root-mean-square errors are given for different Gauss and collocation points (CPs). Convergence rate using distinct numbers of nodal points is calculated, which is nearly equal to 2.
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| contributor author | Amin, Rohul | |
| date accessioned | 2025-08-20T09:24:35Z | |
| date available | 2025-08-20T09:24:35Z | |
| date copyright | 3/4/2025 12:00:00 AM | |
| date issued | 2025 | |
| identifier issn | 1555-1415 | |
| identifier other | cnd_020_04_041004.pdf | |
| identifier uri | http://yetl.yabesh.ir/yetl1/handle/yetl/4308231 | |
| description abstract | In this article, a numerical scheme is developed for the solution of sixth-order boundary value problems (BVP). The Haar collocation method is developed for both linear and nonlinear boundary value problems. In this method, the sixth-order derivative in boundary value problem is approximated using Haar functions, and integration is used to obtain the values of lower derivatives and approximate solution. Some examples are given for the convergence of the proposed method. The Haar technique devoted in this paper is compared with Septic spline method, Sine–Galerkin method, and decomposition method. Maximum absolute and root-mean-square errors are given for different Gauss and collocation points (CPs). Convergence rate using distinct numbers of nodal points is calculated, which is nearly equal to 2. | |
| publisher | The American Society of Mechanical Engineers (ASME) | |
| title | Haar Wavelet Method for the Solution of Sixth-Order Boundary Value Problems | |
| type | Journal Paper | |
| journal volume | 20 | |
| journal issue | 4 | |
| journal title | Journal of Computational and Nonlinear Dynamics | |
| identifier doi | 10.1115/1.4067859 | |
| journal fristpage | 41004-1 | |
| journal lastpage | 41004-8 | |
| page | 8 | |
| tree | Journal of Computational and Nonlinear Dynamics:;2025:;volume( 020 ):;issue: 004 | |
| contenttype | Fulltext |