An innovative Fibonacci wavelet collocation method for the numerical approximation of Emden-Fowler equations

This article presents a novel approach using the Fibonacci wavelet collocation method (FWCM) for the numerical solution of Emden -Fowler -type equations. The Emden -Fowler equations are a class of nonlinear differential equations that arise in various fields of science and engineering, particularly in astrophysics and fluid dynamics. Due to their nonlinear and singular nature, the conventional approaches to solving these equations encounter difficulties. This method is particularly effective in handling problems with singularities, as it adapts naturally to the local behaviour of the solution. Here, we introduced the Fibonacci wavelet collocation method as a powerful numerical technique for tackling Emden -Fowler -type equations. The Fibonacci wavelet basis functions possess remarkable properties, including compact support, making them well -suited for approximating solutions to differential equations. The main advantage of this approach lies in its ability to reduce the computational complexity associated with solving EmdenFowler equations, resulting in accurate and efficient solutions. Comparative analyses with other established numerical methods reveal its superior accuracy and convergence rate performance. Further, several examples demonstrate the method's flexibility when dealing with different singularity levels. This paper contributes to numerical analysis by introducing the Fibonacci wavelet method as a robust tool for solving Emden -Fowler -type equations.