ABSTRACT
Singular second-order nonlinear initial value problems (IVPs) describe several phenomena in mathematical physics and astrophysics. Many problems in astrophysics may be modeled by second-order ordinary differential equations as proposed by Lane. The Emden–Fowler equation has been studied in detail by Emden and Fowler. The Emden–Fowler-type equations are applicable to the theory of stellar structure, thermal behavior of a spherical cloud of gas, isothermal gas spheres, and theory of thermionic currents. The solution of differential equations with singularity behavior in various linear and nonlinear IVPs of astrophysics is a challenge. This chapter utilizes multilayer artificial neural network (ANN) and single-layer functional link artificial neural network models to handle homogeneous and nonhomogeneous Emden–Fowler equations. It also utilizes the feed-forward neural network model with error back-propagation algorithm for modifying the network parameters and minimizing the computed error function. Initial weights of the ANN model are considered as random.
