Abstract
The current research introduces a novel approach to address the computational challenges associated with solving the Lane–Emden‐type equations by transforming them from their conventional differential form to the corresponding integro‐differential form. These equations have wide‐ranging applications in physical sciences, including modeling diffusion phenomena and thermal gradients. We utilize the Volterra integro‐differential (VID) form to resolve computational challenges due to singularity issues. Through the Scale 3 Haar Wavelet (S3‐HW) algorithm, we transform the VID equations into algebraic form and obtain solutions using the Gauss‐elimination method. The quasilinearization technique is implemented whenever a nonlinearity is encountered. Comparative analysis against various techniques demonstrates the superior accuracy and efficiency of our method. Despite challenges such as the discontinuity of Scale 3 Haar Wavelets and singularity issues of Lane–Emden‐type equations, our algorithm paves the way for extending its application to a wide range of physical problems.