@Article{cmes.2005.009.255,
AUTHOR = {Chein-Shan Liu},
TITLE = {Nonstandard Group-Preserving Schemes for Very Stiff Ordinary Differential Equations},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {9},
YEAR = {2005},
NUMBER = {3},
PAGES = {255--272},
URL = {http://www.techscience.com/CMES/v9n3/29759},
ISSN = {1526-1506},
ABSTRACT = {The group-preserving scheme developed by Liu (2001) for calculating the solutions of <i>k</i>-dimensional differential equations system adopted the Cayley transform to formulate the Lie group from its Lie algebra A ∈ <i>so(k,1)</i>. In this paper we consider a more effective exponential mapping to derive exp(<i>h</i>A). In order to overcome the difficulty of numerical instabilities encountered by employing group-preserving schemes on stiff differential equations, we further combine the nonstandard finite difference method into the group-preserving schemes to obtain unconditional stable numerical methods. They provide single-step explicit time integrators for stiff differential equations. Several numerical examples are examined, some of which are compared with exact solutions showing that the nonstandard group-preserving schemes have good computational efficiency and certain accuracy.},
DOI = {10.3970/cmes.2005.009.255}
}