Reconstruction of the Boundary Condition of the Convection–Diffusion–Reaction Equation with Automatic Selection of the Step Length

Predicting water quality in shallow bodies of water can become very complex due to the information required by the different existing models. Sometimes, the data coming from the measurement stations is incomplete due to the stations’ failures. To overcome this drawback, a method is presented that reconstructs the boundary condition of the one-dimensional convection–diffusion and reaction using the adjoint equation. The approach also incorporates the automatic choice of the necessary step length in the descending gradient. The results demonstrated that the implemented technique allows reconstruction and recovery of the boundary condition and the target, respectively, with little computational effort. The convergence of the results tends to be immediate due to the optimal choice in each iteration of the step length, avoiding the difficult task of doing it by trial and error. The results also showed that the more discontinuous the boundary condition, the more complicated its reconstruction will be.