Simultaneous numerical solutions of differential equations of a geodetic line in combination with surface calculation

The purpose of this paper is to present a new method for simultaneous numerical solutions of differential equations of a geodetic line in combination with surface calculation. This method was evaluated as a tool for determination of borders between Sweden and the Union of Soviet Socialist Republics but it has not been published yet. This method is superior to the others in the literature, which are limited to calculations of surfaces of a geodetic triangle. There are no restrictions when it comes to the size, to the distances, and more important, the shape of the surface. With one and the same program different, specific, problems can be solved. This can be used in calculation of e.g. only the geodetic lines length. The method also solves the problem of calculating surfaces, limited by geodetic lines on the ellipsoid. In this paper the whole solution of the problem step by step is presented. The results from test calculations are discussed and prove the theoretical model to be correct. In conclusion one can say that the method solves general problems when it comes to calculations on the biaxial ellipsoid.