Linear Approximation of the Nonlinear
Differential Equation and Stability
Abstract
In this article, the differential equation of the population growth and
decay is studied. The stability of the point solutions (singular or equilibrium
points) of this equation are investigated. From this and another example we
conclude that although in many cases we can, but we can not always approximate
a nonlinear differential equation by a linear one. Finally at the end, the
Laplace, Liapounov and Poincare's stabilities are defined and a criterion for
approximating a non linear differential equation by a linear one is given.
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