TY  - EJOU
AU  - Liu, Chein-Shan 

TI  - Nonstandard Group-Preserving Schemes for Very Stiff Ordinary Differential Equations
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2005
VL  - 9
IS  - 3
SN  - 1526-1506

AB  - 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.
KW  - Stiff differential equations
KW  -  nonstandard group-preserving scheme
KW  -  A-stable
KW  -  L-stable

DO  - 10.3970/cmes.2005.009.255