Dimensioning and Calibration of a mathematical model : Case of the Convection model, Constant coefficient diffusion and Dissipation and source term (Republic of Congo)

Author Name(s)

NGOUBOU Roch Corneille, DINGA Jean Bienvenu et NGANGA Dominique

Abstract
This study focuses on the analysis of solutions of differential equations modeling a physical or chemical phenomenon ; This analysis is fundamentally based on a single solution, that of the resolution of the equation Convection, Diffusion and Dissipation at constant coefficient and source term by the method of decomposition of Adomian (Joseph BONAZEBI YINDOULA,2014). This analytical work has shown that the resolution of a differential equation or a differential equation system does not guarantee the reliability of the solution obtained, the latter will have to be validated in terms of :
 Dimensioning ;
 Correlation with an experimental approach ;
 Validation of related data by statistical indices.
The simulation by ground data of the solution of the equation of Convection, Diffusion and Dissipation at constant coefficient and source term resulting from the decomposition of Adomian has highlighted inadequacies of this solution : The existence of negative values on the variable (mass concentration) after digital application of ground data (GPS data) ; The solution resulting from Adomian’s decomposition does not have the dimension of mass concentration and gives dimensional values : Dimensioning problem ; The solution resulting from the decomposition of Adomian has no parameters that characterize the pollutant that can be tracked : Calibration problem. This work is a significant contribution to improving the solution of the Convection, Diffusion and Dissipation equation at constant coefficient and source term derived from the decomposition of Adomian and thus proposes an algorithm of Dimensionand and Calibration of Adomian’s solution.

Keywords

Mathematical Model, Equation to Dimensions, Transcendent Functions.