Efficient hypergeometric wavelet approach for solving lane-emden equations

Abstract

Nonlinear initial / boundary value problems present challenges in solving due to the divergence of coefficients near singular points. This study introduces a novel hypergeometric wavelet-based approach designed to effectively address these equations. The specialized wavelet method efficiently manages singularities, resulting in improved accuracy. To evaluate the precision and effectiveness of this approach, Lane-Emden type problems are solved using the proposed methodology and compared against established benchmarks. Comparative analyses with alternative wavelet methods are conducted, featuring absolute error tables and graphical representations. The findings highlight the exceptional accuracy and efficiency of the proposed method relative to existing approaches. An advantage of this method is its requirement of fewer basis functions, leading to reduced computational time and complexity.