A backward difference formulation for analyzing the dynamics of capital stocks

2022;
: pp. 1–8
Received: July 07, 2021
Revised: November 17, 2021
Accepted: January 19, 2021
1
The Centre of Foundation Studies for Agricultural Science, Universiti Putra Malaysia
2
Faculty of Economics and Muamalat, Universiti Sains Islam Malaysia
3
Faculty of Economics and Muamalat, Universiti Sains Islam Malaysia
4
Faculty of Science and Technology, Universiti Sains Islam Malaysia
5
Faculty of Science and Technology, Universiti Sains Islam Malaysia
6
Institute for Mathematical Research, Universiti Putra Malaysia
7
Kolej Genius Insan, Universiti Sains Islam Malaysia
8
Kolej Genius Insan, Universiti Sains Islam Malaysia

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.

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Mathematical Modeling and Computing, Vol. 9, No. 1, pp. 1–8 (2022)