The current study provides a numerical method that is derived in a backward difference formulation for ordinary differential equations. The proposed method employs a constant step size algorithm of order 12. The backward difference formulation serves as a competitive algorithm for solving ordinary differential equations. In the current study, the backward difference method is used to analyze the dynamics of capital stocks in terms of depreciation rate for the capital–labor ratio. Results provided in this study will validate the accuracy of the backward difference algorithm hence proving it as a viable alternative for analyzing economic problems in the form of ordinary differential equations.