Cliodynamics

An approach and method for mathematical modelling of the process of population variation in the territory of a given state in a given historical period are proposed. The modelling is based on the use of historical and geographical data from individual parts of the analysed territory. The problem is formulated as a boundary-initial value problem, in which the main variable, normalized population, depends not only on time, but also on the spatial coordinates in a given area. The formulated problem is solved using the Finite Element Method in combination with the finite difference method of integration over time. Dedicated software was developed to perform numerical modelling. As an example, the dynamics of population variation in the territory of the state of the Kyiv princes in the period 700-1015 AD is considered. According to the results of the calculations, the locations of town origins are determined. A comparison of the coordinates of such areas with the real coordinates of the location of towns in a given historical period showed satisfactory quality of modelling.