Solution of singular equation by He’s variational iteration method. (English) Zbl 1401.65089

Summary: A In this paper, we apply He’s variational iteration method (VIM) to investigate singular equations. The approach also introduces a transformation which is required for the conversion of such equations to a first order initial value problem (IVP) and an appropriate framework designed to overcome the difficulty of the singular point at \(x = 0\). The proposed VIM is applied to the reformulated IVP which gives the solution in terms of transformed variable. The desired series solution is obtained by making use of the inverse transformation. The suggested algorithm is tested on Flierl-Petviashivili (FP) equation, Lane-Emden type equation of order \(m\) and a second-order singular IVP.


65L99 Numerical methods for ordinary differential equations
34A45 Theoretical approximation of solutions to ordinary differential equations
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