The Least Square Method for Systems of Linear Ordinary Differential Equations

Some techniques for applying the least square method to solve boundary value problems for overdetermined systems of linear ordinary differential equations with redundant boundary conditions are considered. Problems of this type may have no solution in the general case. Within these techniques for the above problems, the variational approach is applied to both systems of equations and relevant boundary conditions. In one of these techniques, the order of equations of the system under consideration is increased; in this case, additional boundary conditions are set for it. Model examples of applying the techniques and their comparison are given.