ABSTRACT
Many problems in astrophysics and mathematical physics can be modeled by initial or boundary value problems, namely, as second-order nonlinear ordinary differential equations (ODEs). In astrophysics, the equation that describes the equilibrium density distribution in a self-gravitating sphere of polytrophic isothermal gas was proposed by Lane and further described by Emden, which is now known as the Lane–Emden equation. These Lane–Emden-type equations are singular. So the analytical solution of this type of equation is possible in the neighborhood of the singular point. This chapter aims to use multilayer artificial neural network (ANN) and single-layer functional link artificial neural network models for solving homogeneous and nonhomogeneous Lane–Emden equations. Various ANN models are used here to overcome singularity. The chapter utilizes the unsupervised version of error back-propagation algorithm for minimizing the error function and updating the network parameters. Initial weights from the input layer to the output layer are considered as random.
