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Xcas as a Programming Environment for Stability Conditions for a Class of Differential Equation Models in Economics

2011; American Institute of Physics; Linguagem: Inglês

10.1063/1.3636951

1935-0465

George Halkos, Kyriaki Tsilika, Theodore E. Simos, George Psihoyios, Ch. Tsitouras, Zacharias Anastassi,

Economic theories and models

In this paper we examine the property of asymptotic stability in several dynamic economic systems, modeled in ordinary differential equation formulations of time parameter t. Asymptotic stability ensures intertemporal equilibrium for the economic quantity the solution stands for, regardless of what the initial conditions happen to be. Existence of economic equilibrium in continuous time models is checked via a Symbolic language, the Xcas program editor. Using stability theorems of differential equations as background a brief overview of symbolic capabilities of free software Xcas is given. We present computational experience with a programming style for stability results of ordinary linear and nonlinear differential equations. Numerical experiments on traditional applications of economic dynamics exhibit the simplicity clarity and brevity of input and output of our computer codes.