2014/06/10 by Filipov, Stefan M., Gospodinov, Ivan D., Farago, Istvan
#65Lxx #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.1406.2615
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.