Abstract
In this paper, we employ the variational iteration method (VIM) for solving systems of nonlinear equations of Emden-Fowler type of third-order which arise in many scientific applications. The third-order Emden-Fowler equation is characterized by two models, where the shape factor appears twice in the first model, and once in the second. The VIM handles these kinds of shape factors, and overcomes the singularity at the origin. We will use the proper Lagrange multiplier for each model. We solve several complex numerical examples obtaining a rapidly convergent sequence of approximations as the solution. In all examples investigated, we achieved approximations with a high level, thus confirming that only a few variational iterations can provide an accurate approximation.
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