Haar wavelet collocation method for the approximate solutions of Emden-Fowler type equations

Abstract

This paper investigates the Haar wavelet collocation method (HWCM) to obtain approximate solution of the linear Emden-Fowler type equations. To show the efficiency and accuracy of the proposed method, some problems are solved and the obtained solutions are compared with the approximate solutions obtained by using the other numerical methods as well as the exact solutions of the problems.

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

“…For these kinds of problem convergence is directly affected by the small parameters. So, Different numerical solutions have been investigated by the researchers for the solution of this particular kind of problems, homotopy analysis method (Singh, 2018), Genocchi operational matrix for solving Emden-fowler equations (Isah and Phang, 2020) it includes quartic polynomial spline method, fourth order B-spline method (Caglar et al, 1999;Akram, 2011), modifies Adomian decomposition method, differential transformation method, variational iteration method (Khuri, 2001;Hasan and Zhu, 2009;Aruna and Kanth, 2013;Wazwaz, 2015a;Wazwaz, 2015b), In the research article Haar scale wavelet method is discussed for obtaining the approximate solution of linear Emdenfowler equations (Alkan, 2017), Emden fowler equation is solved by using HSWM combined with Newton Raphson method and for solving nonlinearity quasi-linearisation technique is used and discussed some special cases of Emden-fowler equation (Verma and Kumar, 2019), Fourth order Emden-fowler equation is discussed using Haar scale collocation method and by converting the differential equation in to set of algebraic equations and through various examples discuss the applicability of the proposed technique (Khan et al, 2017),Third order differential equations are solved using Haar scale wavelet method, through different examples discussed the effectiveness of the method for solving higher order differential equations (Singh and Kaur, 2021), in the study the author developed the solution of higher order boundary value problem using Haar scale wavelet method (Heydari et al, 2022). Fourth order Lane-Emden fowler equation also described by two different methods adomain decomposition and quintic B-spline method (Ali et al, 2022).…”