Higher resolution methods based on quasilinearization and Haar wavelets on Lane–Emden equations

Abstract

Computing solutions of singular differential equations has always been a challenge as near the point of singularity it is extremely difficult to capture the solution. In this research paper, Haar wavelet coupled with quasilinearization approach (HWQA) is proposed for computing numerical solution of nonlinear SBVPs popularly also referred as Lane–Emden equations. This technique is the combination of quasilinearization and Haar wavelet collocation method. To show the accuracy of the HWQA, several examples are presented. Convergence of the proposed method is also established in this paper, which shows that proposed method converges very fast.

On some computational aspects of Hermite & Haar wavelets on a class of nonlinear singular BVPs

“…All these based on wavelets show high accuracy. In [10,32,33] Haar wavelets are used to solve SBVPs efficiently for higher resolution. Reader may also refer the papers based on Haar wavelets to solve various type of nonlinear problems [2,3,4,39,40,41].…”

A numerical study of boundary layer flow of viscous incompressible fluid past an inclined stretching sheet and heat transfer using nonpolynomial spline method

“…43,44 Many authors have applied this technique to solve the nonlinear ordinary and partial differential equations. [45][46][47] In the present paper, we aim to reconsider the work done by Misra et al 27 and solve using a new proposed method. We investigate the problem of the boundary layer flow of viscous incompressible fluid as proposed in Misra et al 27 Using a similarity transformation, we transform the governing equations with relevant boundary conditions into third-order ordinary differential equation.…”

“…In recent years, there has been an increasing interest to solve the nonlinear differential equation by converting into a sequence of linear differential equation using the quasilinearization technique 43,44 . Many authors have applied this technique to solve the nonlinear ordinary and partial differential equations 45‐47 …”

A note on variation iteration method with an application on Lane–Emden equations

“…Several techniques (analytical/numerical) developed to deal with this type of equations, like monotone iterative technique coupled with upper/lower solutions (Singh and Verma, 2017;Singh et al, 2015;Verma, 2011Verma, , 2012Pandey and Verma, 2011), shooting method (Russell and Shampine, 1975), finite-difference method (Chawla and Katti, 1985;Pandey, 1997;Pandey and Singh, 2004), B-splines and cubic splines method (Chawla and Subramanian, 1988;Kanth and Bhattacharya, 2006), Haar wavelet (Verma and Tiwari, 2019;Swati et al, 2020;Verma et al, 2020b), etc.…”