Mathematical modelling in the river pollution: One dimensional advection diffusion of river pollution in semi infinite media inverse Laplace transforms

Effective tools to simulate and predict pollutant transport in water environments, especially rivers, are water quality models, which can contribute to saving the cost of labour and materials for a large number of chemical experiments to some degree. Due to special environmental pollution issues, water quality models have become very important in some cases. This paper identifies water pollution as a problem. Water quality models have become an important tool for recognizing the behaviours of pollutants in the water environment. In this research, there are general one-dimensional advection diffusion purposes to be resolved. The analytical solution of the model is found using the Laplace Transform method. These results are compared to those obtained by using a classical least square regularized method. For the graph of the solution, we interpret and discuss the concentration of the pollutant against time (t).