Dams and reservoirs are important structures to the development of many societies. This infrastructure provides water for domestic, commercial and industrial consumption, power generation and irrigation. Moreover, dams supply security against droughts and protection from floods. In the matter, inverse modeling of runoff entering a reservoir is a crucial problem to define operational policies in order to avoid floods. The traditional numerical method to estimate these hydrographs is based in the trapezoidal rule. This method is widely used in despite of its disadvantages which are related with: spurious oscillations and with an overestimation of hydrographs peaks. In this work, a comparative analysis based in the integral time square error is developed considering the trapezoidal rule and a central differences scheme.