Title: A spline collocation approach for a business cycle model with small gestation period in production

Authors: Hussain Ibdah; Suheil A. Khuri; Ali Sayfy

Addresses: Department of Mathematics and Statistics, American University of Sharjah, UAE ' Department of Mathematics and Statistics, American University of Sharjah, UAE ' Department of Mathematics and Statistics, American University of Sharjah, UAE

Abstract: A B-spline collocation approach is presented for the numerical solution of a business cycle model with a small gestation period in production. The differential equation that models the problem comprises of a nonlinearity that can arise either from the dependence of investment on profits, a Kaldorian-type model, or on capital stocks. The efficiency of the scheme is tested on a number of special cases; it is shown that the nonlinearity leads to a conditionally stable cycle. The rate of convergence is discussed theoretically and verified numerically to be of fourth-order.

Keywords: B-spline collocation; business cycles; modelling; nonlinear differential equations; delay; convergence rate; gestation period; production.

DOI: 10.1504/IJDSDE.2016.077251

International Journal of Dynamical Systems and Differential Equations, 2016 Vol.6 No.2, pp.101 - 116

Received: 16 Jun 2015
Accepted: 13 Aug 2015

Published online: 21 Jun 2016 *

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