@Article{cmes.2008.026.157,
AUTHOR = {Chein-Shan Liu},
TITLE = {A Lie-Group Shooting Method for Computing Eigenvalues and Eigenfunctions of Sturm-Liouville Problems},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {26},
YEAR = {2008},
NUMBER = {3},
PAGES = {157--168},
URL = {http://www.techscience.com/CMES/v26n3/25110},
ISSN = {1526-1506},
ABSTRACT = {For the Sturm-Liouville eigenvalues problem we construct a very effective Lie-group shooting method (LGSM) to search the eigenvalues, and when eigenvalue is determined we can also search a missing left-boundary condition of the slope through a weighting factor <i>r ∈ (0,1)</i>. Hence, the eigenvalues and eigenfunctions can be calculated with a better accuracy. Because a closed-form formula is derived to calculate unknown slope in terms of λ for the estimation of eigenvalues, the present method is easy to implement and has a low computational cost. Similarly by applying the LGSM to find a corresponding eigenfunction in terms of λ is easily carried out in a finer range of <i>r</i>. Numerical examples were examined to show that the Lie-group shooting method has a significantly improved accuracy than before.},
DOI = {10.3970/cmes.2008.026.157}
}