The one-dimensional advection-diffusion-reaction equation is a mathematical model describing transport and diffusion problems\nsuch as pollutants and suspended matter in a stream or canal. If the pollutant concentration at the discharge point is not uniform,\nthen numerical methods and data analysis techniques were introduced. In this research, a numerical simulation of the onedimensional\nwater-quality model in a stream is proposed. The governing equation is advection-diffusion-reaction equation with\nnonuniform boundary condition functions. The approximated pollutant concentrations are obtained by a Saulyev finite difference\ntechnique. The boundary condition functions due to nonuniform pollutant concentrations at the discharge point are defined by\nthe quadratic interpolation technique. The approximated solutions to the model are verified by a comparison with the analytical\nsolution. The proposed numerical technique worked very well to give dependable and accurate solutions to these kinds of several\nreal-world applications.
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