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.
Highlights
Boundary value problems (BVPs) with higher order arise in the field of astrophysics, and the narrow convecting layers bounded by stable layers, which are believed to surround A-type stars, may be modeled by tenth order BVPs
We developed the Haar wavelet collocation method (HWCM) for the numerical simulation of 10th-order BVPS of ordinary differential equations
The maximum absolute errors for distant number of discrete collocation point (CP) and Gauss points (GPs) are shown for each example in tables
Summary
Rohul Amin 1 , Kamal Shah 2 , Imran Khan 1 , Muhammad Asif 1 , Mehdi Salimi 3,4, *.
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