A Comparative Study using Scale-2 and Scale-3 Haar Wavelet for the Solution of Higher Order Differential Equation-Reference-Cited by-同舟云学术

A Comparative Study using Scale-2 and Scale-3 Haar Wavelet for the Solution of Higher Order Differential Equation

Published:2023-10-01 Issue:5 Volume:8 Page:966-978
ISSN:2455-7749
Container-title:International Journal of Mathematical, Engineering and Management Sciences
language:en
Short-container-title:Int. j. math. eng. manag. sci.

Author:

Kumar Ratesh¹,Gupta Jaya²

Affiliation:

1. Department of Mathematics, Lovely Professional University, Phagwara, 144411, Punjab, India.

2. Department of Mathematics, Lovely Professional University, Phagwara, 144411, Punjab, India,

Abstract

A comparative study of scale-2 and scale-3 Haar wavelet has been presented to illustrate the level of accuracy attained by both the wavelets by applying on higher order differential equations known as Emden fowler equation, which has great importance in the field of astrophysics. Approximation of space variable is done by scale-2 and scale-3 Haar wavelet method by choosing different scales. The method is tested upon several test problems. The results are computed and compared in the form of absolute errors. The numerical tests confirm the accuracy, applicability and efficiency of the proposed method with different levels using both the wavelets. By the help of MATLAB algorithm simplification of the computational process is done.

Publisher

Ram Arti Publishers

Subject

General Engineering,General Business, Management and Accounting,General Mathematics,General Computer Science

Reference24 articles.

1. Akram, G. (2011). Quartic spline solution of a third order singularly perturbed boundary value problem. ANZIAM Journal, 53, E44-E58. https://doi.org/10.21914/anziamj.v53i0.4526.

2. Ali, K.K., Mehanna, M.S., Abdelrahman, M.I., & Shaalan, M.A. (2022). Analytical and numerical solutions for fourth order Lane–Emden–Fowler equation. Partial Differential Equations in Applied Mathematics, 6, 100430.

3. Alkan, S. (2017). Haar wavelet collocation method for the approximate solutions of Emden-Fowler type equations. Natural and Engineering Sciences, 2(3), 37-44.

4. Arora, G., Kumar, R., & Kaur, H. (2018). A novel wavelet-based hybrid method for finding the solutions of higher order boundary value problems. Ain Shams Engineering Journal, 9(4), 3015-3031.

5. Aruna, K., & Kanth, A.R. (2013). A novel approach for a class of higher order nonlinear singular boundary value problems. International Journal of Pure and Applied Mathematics, 84(4), 321-329.