Abstract
The study of interactions between the economy and the environment has always been an interesting subject. Apart from static input–output (IO) models, environmentally extended IO analysis has resulted in dynamic IO models as well. Dynamic models are built of differential equations and, in the case of discrete models with the help of difference equations. The dynamic approach requires advanced mathematical skills especially in cases where the stability of the system under study is considered. In this paper we state some applied environmental models in discrete time based on dynamic IO analysis and we propose a computational approach in computer algebra system environments that investigates the extent and the nature of their stability. The computer codes are fully presented and can be reproduced as they are in computational-based research practice and education.
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Notes
Mathematica software is tradable from Wolfram Research, Inc.
Xcas is a Computer Algebra System available free in http://www-fourier.ujf-grenoble.fr/~parisse/giac.html.
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Appendix: Mathematica and Xcas Programmed Functions
Appendix: Mathematica and Xcas Programmed Functions
In this appendix we provide a brief overview of the code we used for the examples in this paper.
The first argument of steadytate function in Mathematica contains system’s coefficient matrix (a) and the second argument system’s initial state (initial) in a column matrix form. steadytate function calculates the asymptotic behavior of the system in a column matrix form.
distributionk function, takes as arguments system’s coefficient matrix (a) and system’s initial state (initial).
In Xcas environment, stability conditions are examined using stabilitytest2 function taking system’s coefficient matrix as argument (x). steadystate function takes as arguments system’s coefficient matrix (a) and the system’s initial state (initialstate) in a column matrix form.
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Halkos, G., Tsilika, K. Dynamic Input–Output Models in Environmental Problems: A Computational Approach with CAS Software. Comput Econ 47, 489–497 (2016). https://doi.org/10.1007/s10614-015-9497-4
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DOI: https://doi.org/10.1007/s10614-015-9497-4