In this paper, an approach based on the variational iteration method (VIM) is proposed
with an auxiliary parameter to predict the multiplicity of the solutions of homogeneous nonlinear
ordinary differential equations with boundary conditions. The proposed approach is capable to pre-
dict and calculate all branches of the solutions simultaneously. Four practical problems are chosen
to show the efficiency and importance of the proposed method. The proposed approach successfully
detects multiple solutions to Bratu’s problem, the model of mixed convection flows in a vertical
channel, the nonlinear model of diffusion and reaction in porous catalysts and the nonlinear reac-
tive transport model.