Shooting-Projection Method for Two-Point Boundary Value Problems
Numerical Analysis
2017-02-08 v4
Abstract
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.
Cite
@article{arxiv.1406.2615,
title = {Shooting-Projection Method for Two-Point Boundary Value Problems},
author = {Stefan M. Filipov and Ivan D. Gospodinov and Istvan Farago},
journal= {arXiv preprint arXiv:1406.2615},
year = {2017}
}