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Abstract
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The study of singular fourth-order Emden–Fowler equations is of fundamental importance due to their widespread occurrence in applied mathematics, physics, and engineering. These equations arise in diverse contexts such as astrophysics (stellar structure models), nonlinear diffusion processes, fluid mechanics, reaction-diffusion systems, and thermal explosion theory. Their singular nature, coupled with higher-order derivatives, makes them challenging to analyze and solve using standard analytical and numerical techniques.
Conventional methods—such as finite differences, finite elements, or spectral approaches—often struggle with accuracy, stability, and computational efficiency when applied to singular problems of this type. Particularly, the singularities in the coefficients or solutions near boundary points cause numerical instability and reduce convergence rates. Thus, there is a pressing need for more robust, stable, and efficient computational techniques capable of handling singularity-dominated problems while maintaining high precision.
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