Abstract
A non-linear two dimensional convection-dispersion equation (CDE) plays a vital role in most mathematical model. Our study is based on the model arising from water contamination through oil spillage. The model contains the non-constant dispersion. We employ Lie symmetry method to reduce the CDE into a simpler ordinary differential equations (ODEs) and introduce the G/G1 and w = (z′)−1 techniques to determine the exact solutions. Furthermore if the ODE turns to be difficult to solve, we resort to transformation methods which reduce the ODEs to a more simpler first ODEs. Exact solutions are constructed.A non-linear two dimensional convection-dispersion equation (CDE) plays a vital role in most mathematical model. Our study is based on the model arising from water contamination through oil spillage. The model contains the non-constant dispersion. We employ Lie symmetry method to reduce the CDE into a simpler ordinary differential equations (ODEs) and introduce the G/G1 and w = (z′)−1 techniques to determine the exact solutions. Furthermore if the ODE turns to be difficult to solve, we resort to transformation methods which reduce the ODEs to a more simpler first ODEs. Exact solutions are constructed.
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