The objective of this paper is to apply the well-known exact operational matrices (EOMs) idea for solving the Emden-Fowler equations, illustrating the superiority of EOMs versus ordinary operational matrices (OOMs). Up to now, a few studies have been conducted on EOMs and the differential equations solved by them do not have high-degree nonlinearity and the reported results are not regarded as ...

Abstract The aim of the current study is to present numerical solutions a nonlinear second-order coupled Emden–Fowler equation by developing neuro-swarming-based computing intelligent solver. feedforward artificial neural networks (ANNs) are used for modelling, and optimization carried out local/global search competences particle swarm (PSO) aided with capability interior-point method (IPM), i....

This paper is devoted to proposing numerical algorithms based on the use of tau and collocation procedures, two widely used spectral approaches for treatment initial high-order linear non-linear equations singular type, especially those Emden–Fowler type. The class modified Chebyshev polynomials third-kind constructed. generalizes polynomials. A new formula that expresses first-order derivative...

The homotopy analysis method [1, 2], is developed to search the accurate asymptotic solutions of nonlinear problems. This technique has been successfully applied to many nonlinear problems such as the viscous flows of non-Newtonian fluids [3, 4], the Korteweg-de Vries-type equations [5, 6], nonlinear heat transfer [7, 8], finance problems [9, 10], Riemann problems related to nonlinear shallow w...

This work aims at a new semi-analytical technique called the Adomian decomposition method for analysis of time-fractional Emden–Fowler equations. The Laplace transformation and iterative are implemented to obtain result given models. suggested has edge over other methods, as it does not need extra materials calculations. presented validity is demonstrated by examining four mathematical Due stra...