A new technique for solving singular IVPs of Emden-Fowler type
Provides a new analytical tool for nonlinear differential equations, but the improvement is incremental for a specific problem class.
The paper introduces the optimal perturbation iteration method for solving singular initial value problems of Emden-Fowler type, demonstrating high accuracy and convergence control compared to existing methods.
A new analytic approximate technique for addressing nonlinear problems, namely the optimal perturbation iteration method, is introduced and implemented to singular initial value Lane-Emden type problems to test the effectiveness and performance of the method. This technique provides us to adjust the convergence regions when necessary.Comparing different methods reveals that the proposed method is highly accurate and has great potential to be a new kind of powerful analytical tool for nonlinear differential equations.