Numerical determination of the geodesic curves: the solution of a twopoint boundary value problem

In this paper, we suggest a simple iterative method to find the geodesic path on a surface parameterized byorthogonal curvilinear system between two given points based on solving Boundary Value Problem. In thissupposed method, an iterative algorithm is used for finding the sufficient initial values as the destinationpoint agree with the boundary conditions. Geodesic determination between two given points is formulatedfor a general surface, and specially tested for reference ellipsoid which has many applications ingeosciences and geodesy. Accuracy of the method is independent on the distant between two points on thesurface. Moreover, it can be used in aviation and sailings for finding the shortest path between start anddestination points.