Semilinear elliptic equations are ubiquitous in natural sciences. They give rise to a variety of important phenomena in quantum mechanics, nonlinear optics, astrophysics, etc because they have rich multiple solutions. But the nontrivial solutions of semilinear equations are hard to be solved for the lack of stabilities, such as Lane-Emden equation, Henon equation and Chandrasekhar equation. In ...

We obtain the optimal system’s generating operators associated to a modification of generalization Emden–Fowler Equation. Using those we characterize all invariant solutions generalized. Moreover, present variational symmetries and corresponding conservation laws, using Noether’s theorem Ibragimov’s method. Finally, classify Lie algebra given equation.

in this paper, the ultraspherical operational matrices of derivatives are constructed. based on these operational matrices, two numerical algorithms are presented and analyzed for obtaining new approximate spectral solutions of a class of linear and nonlinear lane-emden type singular initial value problems. the basic idea behind the suggested algorithms is basically built on transforming the eq...

arises in the study of gas dynamics and fluids mechanics, and in the study of relativistic mechanics, nuclear physics, and chemically reacting system see, e.g., 1 and the references therein for the continuous model. The negative exponent Emden-Fowler equation α < 0 has been used in modeling non-Newtonian fluids such as coal slurries 2 . The physical interest lies in the existence of positive so...

Second order ordinary differential equations that possesses the constant invariant are investigated. Four basic types of these were found. For every type complete list nonequivalent is issued. As exampes equivalence problem for Painleve II equation, III equation with three zero parameters, Emden and some other solved.

A numerical method to solve Lane-Emden equations as singular initial value problems is presented in this work. This method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The collocation method transforms the differential equation into a system of algebraic equations. It also has application in a wide area...

The isothermal gas sphere is a particular type of Lane-Emden equation and used widely to model many problems in astrophysics, like the formation stars, star clusters galaxies. In this paper, we present computational scheme simulate conformable fractional using an artificial neural network (ANN) technique, compare obtained results with analytical solution deduced Taylor series. We performed our ...