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Analytical solution for the time-dependent Emden-Fowler type of equations by variational iteration method

The variational iteration method (VIM) is applied to obtain analytical solutions for the time-dependent Emden-Fowler type equations and wave-type equations with singular behavior. In this method, general Lagrange multipliers are introduced to construct correction functional and identified optimally via variational theory for the problems. It is well known that one of the advantages of the variational iteration method is the free choice of initial approximation. Therefore, we use this advantage to construct initial values without unknown parameters. Some of the nonlinear and linear equations are examined by the modified method to illustrate the effectiveness and convenience of the method in solving equations with singularity, where the convergence of the result is observed.