@Article{cmes.2006.015.069,
AUTHOR = {Chein-Shan Liu},
TITLE = {Efficient Shooting Methods for the Second-Order Ordinary Differential Equations},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {15},
YEAR = {2006},
NUMBER = {2},
PAGES = {69--86},
URL = {http://www.techscience.com/CMES/v15n2/26680},
ISSN = {1526-1506},
ABSTRACT = {In this paper we will study the numerical integrations of second order boundary value problems under the imposed conditions at <i>t=0</i> and <i>t=T</i> in a general setting. We can construct a compact space shooting method for finding the unknown initial conditions. The key point is based on the construction of a one-step Lie group element <b>G(u<sub>0</sub>,u<sub><i>T</i></sub>)</b> and the establishment of a mid-point Lie group element <b>G(<i>r</i>)</b>. Then, by imposing <b>G(u<sub>0</sub>,u<sub><i>T</i></sub>)</b> = <b>G(<i>r</i>)</b> we can search the missing initial conditions through an iterative solution of the weighting factor <i>r</i> ∈ (0,1). Numerical examples were examined to convince that the new approach has high efficiency and accuracy with a fast convergence speed by solving <i>r</i> with a half-interval method. Even under a large span of the boundary coordinate, the new method is also applicable by requiring only a few iterations. The method is also extended to the BVP with general boundary conditions.},
DOI = {10.3970/cmes.2006.015.069}
}