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    The Lie-Group Shooting Method for Singularly Perturbed Two-Point Boundary Value Problems

    Chein-Shan Liu1

    CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.3, pp. 179-196, 2006, DOI:10.3970/cmes.2006.015.179

    Abstract This paper studies the numerical computations of the second-order singularly perturbed boundary value problems (SPBVPs). In order to depress the singularity we consider a coordinate transformation from the x-domain to the t-domain. The relation between singularity and stiffness is demonstrated, of which the coordinate transformation parameter λ plays a key role to balance these two tendencies. Then we construct a very effective Lie-group shooting method to search the missing initial condition through a weighting factor r ∈ (0,1) in the t-domain formulation. For stabilizing the new method we also introduce two new systems by a translation of the dependent variable.… More >

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