## Least Squares Spectral Collocation Method for Solving Identification Problems in a Lake Pollution Model over a Complex Domain

 AUTHOR(S): Aboubakari Traore, Benjamin Mampassi TITLELeast Squares Spectral Collocation Method for Solving Identification Problems in a Lake Pollution Model over a Complex Domain PDF KEYWORDSLake Pollution, Least-squares formulation, finite elements, Collocation point methods, differentiation matrices, complex domain ABSTRACTIn this paper, We modeled the behavior of pollution concentration in a lake by a parabolic equation. The domain of the lake is reduced to 2D-dimension in space and characterized by some obstacles inside and the circumference is a polygonal form. First, The mathematical model obtained contains unknown parameters which have to be determined and then the approximative solution of the mathematical model has to be estmimated. For this purpose, we approximate the system of equations by means of discrete differential operators adapted to the complexity of the domain based on Least Squares Spectral Collocation Method, LSSCM. To test our numerical scheme, we consider some experimental data. After computations, we obtain optimals values of unknown parameters and the approximative solution of the mathematical model. The 2D and 3D-dimension in space graphics of the solution are presented. The analysis of the graphs allows us to better identify the source of the pollution, the concentration of the pollution and the direction of the propagation in lake. We conclude that the use of Least squares spectral collocation method to solve pollution problem over a complex domain was successful. Cite this paperAboubakari Traore, Benjamin Mampassi. (2017) Least Squares Spectral Collocation Method for Solving Identification Problems in a Lake Pollution Model over a Complex Domain. International Journal of Mathematical and Computational Methods, 2, 19-30