We present a detailed analysis of general relativistic static spherical symmetric distribution in which both the radial and tangential pressures follow master polytropic equation state that generalizes standard treatment avoids appearance singularities system. In particular, we find corresponding Lane-Emden integrate it for wide range values parameters involved. explore parameter space with aim...

A numerical method based on Legendre multi-wavelets is applied for solving Lane-Emden equations which form Volterra integro-differential equations. The Lane-Emden equations are converted to Volterra integro-differential equations and then are solved by the Legendre multi-wavelet method. The properties of Legendre multi-wavelets are first presented. The properties of Legendre multi-wavelets are ...

Abstract In this work, a nonlinear singular variable-order fractional Emden–Fowler equation involved with derivative non-singular kernel (in the Atangana–Baleanu–Caputo type) is introduced and computational method proposed for its numerical solution. The desired established upon shifted Jacobi polynomials their operational matrix of differentiation (which extracted in present study) together sp...

The objective of this paper is applying the well-known exact operational matrices (EOMs) idea for solving the Emden-Fowler equations, illustrating the superiority of EOMs over ordinary operational matrices (OOMs). Up to now, a few studies have been conducted on EOMs ; but the solved differential equations did not have high-degree nonlinearity and the reported results could not strongly show the...

In this paper, we compute and visualize solutions of several major types of semilinear elliptic boundary value problems with a homogeneous Dirichlet boundary condition in 2D. We present the mountain–pass algorithm (MPA), the scaling iterative algorithm (SIA), the monotone iteration and the direct iteration algorithms (MIA and DIA). Semilinear elliptic equations are well known to be rich in thei...

The aim of the present study is to a new model based on nonlinear singular second order delay differential equation Lane–Emden type and numerically solved by using heuristic technique. Four different examples are presented designed artificial neural networks optimized global search, local search methods their hybrid combinations, respectively, named as genetic algorithm (GA), sequential quadrat...

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...