Applications of Numerical Methods with Linear Complexity in Flood Forecasting in Rivers

This present work proposes to estimate the day that the volume of a river will overflow through applications of numerical methods with linear computational complexity. We adopt a theoretical mathematical model that enables us to predict the time of flood, where in the resolutions of the equations that represent the model, numerical methods are applied, in order to identify which one presents better solution, considering the computational effort and precision of the solution, and comparing with the solution proposed by the model. The hydrological model adopted makes the prediction by solving Burgers, however this method has a polynomial complexity O(n^r+1). In this work the viability of using the methods of simple steps, with complexity or order O(n) is verified.