Filipov S.M.Gospodinov I.D.Faragó I.2024-07-102024-07-102024-07-102024-07-102017-10-011873-54520893-965910.1016/j.aml.2017.04.002SCOPUS_ID:85018474005https://rlib.uctm.edu/handle/123456789/428This paper presents a novel shooting method for solving two-point boundary value problems for second order ordinary differential equations. The method works as follows: first, a guess for the initial condition is made and an integration of the differential equation is performed to obtain an initial value problem solution; then, the end value of the solution is used in a simple iteration formula to correct the initial condition; the process is repeated until the second boundary condition is satisfied. The iteration formula is derived utilizing an auxiliary function that satisfies both boundary conditions and minimizes the H1 semi-norm of the difference between itself and the initial value problem solution.enArticle