  This 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.
