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    Nonstandard Group-Preserving Schemes for Very Stiff Ordinary Differential Equations

    Chein-Shan Liu1

    CMES-Computer Modeling in Engineering & Sciences, Vol.9, No.3, pp. 255-272, 2005, DOI:10.3970/cmes.2005.009.255

    Abstract The group-preserving scheme developed by Liu (2001) for calculating the solutions of k-dimensional differential equations system adopted the Cayley transform to formulate the Lie group from its Lie algebra A ∈ so(k,1). In this paper we consider a more effective exponential mapping to derive exp(hA). 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… More >

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