Friday, October 19, 2012

Approximation of exp(x) deduced from the implicit Euler numerical solution of first order linear differential equations


Abstract

In this paper it is shown a simple approximation of the function exp(x) for positive values of x, deduced from the implicit Euler numerical solution of first order lineal differential equations (ODE). The results show that the approximation has an error of less than 10% for exp(x) when x < 0.35 and for exp(-x) when x < 0.5, which is acceptable for many engineering applications, and helps facilitate the analysis of some systems without the use of computers.

Keywords: approximation, Euler implicit method, exponential function, first order ODE.


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