NUMERICAL PREDICTION OF THE IMPACT OF EXPERIMENTAL TIME FOR FIXED PARAMETER VALUES IN THE INTERACTION BETWEEN PM2.5 AND RELATIVE HUMIDITY AS WELL AS THE INTERACTION BETWEEN PM1 AND RELATIVE HUMIDITY

Abstract

In modeling the qualitative characteristic of the impact of experimental time for a fixed parameter value in the interaction between particulate matter (PM_2.5 and PM₁) and meteorological variable (Relative Humidity, RH) over a longer duration of time, It is a good numerical analysis practice that such an event of a complex dynamical system that can not admit an analytic solution for the co-existence steady-state solution, we adopted an alternative method to study the qualitative behavior of the unique positive steady-state solution as ????→∞. This challenging problem was tackled in this study using computational approach. This research work has used the mathematical procedure for parameter estimation using p-vector norm numerical method to selects the precise value of the intra-competition coefficient for the pollutant level PM1 field data which was used in the model equations for various studies and analysis. The appropriate precise value of the intra-competition coefficient β, of the pollutant level PM1 obtained using this method is stated as β= 0.019423899416342. We observed in this study all through our investigations in the interactions between pollutant level PM2.5 and Relative Humidity as well as PM1 and Relative Humidity, on the base day of our experimental time, the initial value here called initial condition (IC) when all model parameter values are fixed in the interaction between PM2.5 and Relative Humidity as well as the interaction between PM1 and Relative Humidity for a time interval 0(30)360 in months, on the based day of our simulation time here called the initial conditions, the valued are recorded as N1(PM2.5)=19.40, N2(Relative Humidity Rh1, for PM2.5-RH Interaction) =62.0, N3(PM1) =6.3, N4(Relative Humidity Rh2 for PM1-RH) =62.0. Furthermore, as the time ranges from the 30th day of our simulation time to an optimal time on the 360th, we observed a fluctuation in the four coordinates from a value of N1(PM2.5) =22.3044, N2(Rh1 for PM2.5-RH) =68.2886, N3(PM1) =15.0348, N4(Rh2 for PM1-RH) =67.7135 to an optimal converging value which saturated at N1(PM2.5)=22.2917, N2(Rh1 for PM2.5-RH) =70.9775, N3(PM1) =15.0231, N4(Rh2 for PM1-RH) =69.8749. This is an indication that the minimum values occur at the initial conditions and the maximum values occurs within the time intervals to an optimal converging value. The full results and discussions of this noble contributions to knowledge all fully presented in this work.