Uniform Haar wavelet technique with Newton’s method for a kind of derivative dependent SBVPs

Abstract

This work deals with the construction of a coupled technique, uniform Haar wavelet and Newton–Raphson method for a kind (Lane–Emden–Fowler type) of two-point derivative dependent singular differential equation $$\begin{aligned}&(g(x)y')'= h(x)f(x,y, g y'), \qquad x\in (0,1] \end{aligned}$$ with Dirichlet and Neumann–Robin boundary conditions (BCs) $$\begin{aligned}&y(0) =a,\qquad y(1)= b,\\&y'(0)= 0,\qquad \alpha _1 y(1)+\beta _1 y'(1)= \gamma _1. \end{aligned}$$ Here $$g(x)>0$$ on (0, 1) permit $$g(0)=0$$ . This collocation based numerical approach is employed for reducing the considered class of singular differential equations into algebraic one and hence, Newton–Raphson method is applied for numerical solution. The convergence study and its error analysis is developed to depict validity and the order of stability of the present method. From practical point of view, some numerical examples (both linear and nonlinear) have been illustrated for demonstrating the simplicity of compliance and outcomes based on the method. The $$L_{2}$$ norm and absolute error assist in demonstrating the enhancement of results with resolution J increases. In addition, the utilization of present method is found to be precise, straightforward, quick, adaptable, helpful, cost-friendly and computationally attractive.