Stability of the linearization method applied in tricom-partmental polynomial catenary systems of order (α + β)

This paper aims to identify exchange coefficients of a nonlinear polynomial tri-compartmental catenary system of (α + β) order. This is based on two principal procedures. The first procedure presented is related to the recommended solution consisting of introducing an adequate time t∗ > 0 in a way to be defined. That is to say: wait a moment to allow the exchange to settle in the polynomial (α +β) order nonlinear catenary system after injecting the quantity into the main compartment, then measure this compartment with compartment 2, at this time t∗ > 0. In the second procedure, we apply the Taylor formula to linearize the nonlinear system and identify the exchange coefficients. In the end, we will prove that the linearization method is stable