Abstract
In this work, we will give a novel method to construct a continuous approximation of the Exponential, Logistic, and Gaussian functions that allow us to do a handmade drawing of their graphs for which there is no accuracy of drawing at elementary levels (even at advanced ones!). This method arises from solving the elementary ordinary differential equation x0 (t) = ax(t) combined with a suitable piecewise constant argument. The proposed approximation will allow us to generate several numerical schemes in an elementary way, generalizing the classical ones as, Euler’s schemes. No sophisticated mathematical tools are needed.
Publisher
Universidad Catolica del Norte - Chile
Reference11 articles.
1. [1] R. Bellman and K. L. Cooke, Modern Elementary Differential Equations, 2nd ed., Dover, 1995.
2. [2] E. A. Coddington, An Introduction to Ordinary Differential Equations. 2nd ed., Dover, 1989.
3. [3] A. Myshkis, "On certain problems in the theory of differential equations with deviating argument", Russian Mathematical Surveys, vol. 32, no. 2, pp. 173-203, 1977.
4. [4] K. Cooke and S. Busenberg, Models of vertical transmitted diseases with sequential-continuous dynamics, in Nonlinear Phenomena in Mathematical Sciences: Proceedings of an International Conference on Nonlinear Phenomena in Mathematical Sciences, Held at the University of Texas at Arlington, June 16-20, 1980, (New York), pp. 179-187, Academy Press, 1982.
5. [5] L. Dai, Nonlinear Dynamics of Piecewise Constant Systems and Implementation of Piecewise Constant Arguments. New York: World Scientific Press, 2008.
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