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Decomposition method for solving a nonlinear business cycle model

Published online by Cambridge University Press:  17 February 2009

Elias Deeba ,
Ghassan Dibeh ,
Suheil Khuri  and
Shishen Xie
Elias Deeba
Affiliation:
Department of Computer and Mathematical Sciences, University of Houston-Downtown, Houston, Texas 77002, USA; e-mail: [email protected] and [email protected].
Ghassan Dibeh
Affiliation:
Department of Economics, Lebanese American University, Byblos, Lebanon; e-mail: [email protected].
Suheil Khuri
Affiliation:
Department of Computer Science, Mathematics and Statistics, AUS, UAE.
Shishen Xie
Affiliation:
Department of Computer and Mathematical Sciences, University of Houston-Downtown, Houston, Texas 77002, USA; e-mail: [email protected] and [email protected].
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Abstract

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In this paper we present a Kaleckian-type model of a business cycle based on a nonlinear delay differential equation. A numerical algorithm based on a decomposition scheme is implemented for the approximate solution of the model. The numerical results of the underlying equation show that the business cycle is stable.

Type
Research Article
Information
The ANZIAM Journal , Volume 45 , Issue 2 , October 2003 , pp. 295 - 302
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Abbaoui, K. and Cherruault, Y., “The decomposition method applied to the Cauchy problem”, Kybernetes 28 (1999) 68–74.Google Scholar
[2]Adomian, G., “A new approach to nonlinear partial differential equations”, J. Math. Anal. Appl. 102 (1984) 420–434.CrossRefGoogle Scholar
[3]Asea, P. K. and Zak, P., “Time-to-build and cycles”, J. Econom. Dynam. Control 23 (1999) 1155–1175.Google Scholar
[4]Casal, A. C. and Dibeh, G., “Functional differential equations modeling in economics and environment”, in Environment, economics and their mathematical models (eds. Diaz, J. I. and Lions, J. L.), (Masson, Paris, 1994) 19–27.Google Scholar
[5]Cherruault, Y., Modeles et methodes mathematiques pour les sciences du vivant (Presses Universitaires de France, Paris, 1998).Google Scholar
[6]Cherruault, Y., Optimisation: methodes locales et globales (Presses Universitaires de France, Paris, 1999).Google Scholar
[7]Cherruault, Y., Saccomandi, G. and Some, B., “New results for convergence of Adomian's method applied to integral equations”, Math. Comput. Modelling 16 (1992) 85–93.CrossRefGoogle Scholar
[8]Cherruault, Y. and Seng, Y., “The resolution of non-linear integral equations of the first kind using the decompositional method of Adomian”, Kybernetes 26 (1997) 198–206.CrossRefGoogle Scholar
[9]Deeba, E. Y., Khuri, S. A. and Xie, S., “An algorithm for solving a nonlinear integro-differential equation”, Appl. Math. Comput. 115 (2000) 123–131.Google Scholar
[10]Dibeh, G., “Time delays and business cycles: Hilferding's model revisited”, Rev. Political Econ. 13 (2001) 329–341.CrossRefGoogle Scholar
[11]Dore, M., The macrodynamics of business cycles (Blackwell, Cambridge, 1993).Google Scholar
[12]Farmer, R. E. A., The macroeconomics of self-fulfilling prophecies, 2nd ed. (MIT Press, Cambridge, 1999).Google Scholar
[13]Kaldor, N., “A model of the trade cycle”, Econom. J. 50 (1940) 78–92.Google Scholar
[14]Kalecki, M., Collected Works, Vol. 1: Capitalism (Oxford Press, New York, 1990).Google Scholar
[15]Khelifa, S. and Cherruault, Y., “New results for the Adomian method”, Kybernetes 29 (2000) 332–355.CrossRefGoogle Scholar
[16]Kydland, F. E. and Prencott, E. C., “Time to build and aggregate fluctuations”, Econometrica 50 (1982) 1345–1369.Google Scholar
[17]Lucas, R. E., “An equilibrium model of the business cycles”, J. Political Econom. 83 (1975) 1113–1144.Google Scholar
[18]Plosser, C., “Understanding real business cycles”, J. Econom. Perspect. 3 (1989) 51–78.Google Scholar
[19]Stiglitz, J. E., “Methodological issues and the new Keynesian economics”, in Macroeconomics: A survey of research strategies (eds. Vercelli, A. and Dimitri, N.), (Oxford Univ. Press, New York, 1992) 38–86.Google Scholar
[20]Taylor, L., Income distribution, inflation and growth (MIT Press, Cambridge, 1991).Google Scholar