A numerical method based on B-spline is developed to solve the time-dependent Emden-Fowler-type equations. We also present a reliable new algorithm based on B-spline to overcome the difficulty of the singular point at 0 x = . The error analysis of the method is described. Numerical results are given to illustrate the efficiency of the proposed method.

We discuss the existence of solutions with oblique asymptotes to a class of second order nonlinear ordinary differential equations by means of Lyapunov functions. The approach is new in this field and allows for simpler proofs of general results regarding Emden-Fowler like equations.

In this article, we presented a new approach deduced from He’s homotopy perturbation method (HPM) to obtain exact and/or approximate analytical solutions of Emden–Fowler type equations. The results reveal that the proposed algorithm is very effective and in most cases yield exact solutions in the first approximation. Some examples are given to illustrate the new approach.

The recently developed theory of quasi-Lie schemes is studied and applied to investigate several equations of Emden type and a scheme to deal with them and some of their generalisations is given. As a first result we obtain t-dependent constants of the motion for particular instances of Emden equations by means of some of their particular solutions. Previously known results are recovered from t...