The study of migratory patterns is important in determining the structure and composition of migrants in the various cities and countries of destination. This can be done by estimating the models proposed by Rogers and Castro (1981) and by the detailed information of the population. There are several studies that treat the problem from the internal migration and its calendars and population projections (Rees 1977; Rogers y Raymer, 2009, Bates J y Brachen I, 1982; Liaw and Nagnur, 1985; Kawabe, 1990), leaving outside the relation with international migration and having troubles with the selectivity of the initial values in the optimization process. The main goal of this study is to estimate the Rogers and Castro equations by solving the initial values problem, which guarantees that the values resulting from the optimization are influenced as little as possible by these values. The data used are the National Institute of Statistics of Spain and correspond to the standardized migration rates for the year 2015 by sex. The results presented in this example are the estimates obtained from the parameters for various types of migration such as interregional, interprovincial and international. Here, differences between the peak ages of labour migration as well as the post-retirement ages are observed. Subsequent work has to do with the refinement of the algorithm, as well as the use of the same for the calculation of temporal series of the parameters that uses information from sources as IPUMS and administrative registries of more countries, thus making comparisons on the performance of various groups of emigrants.