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    Efficient Shooting Methods for the Second-Order Ordinary Differential Equations

    Chein-Shan Liu1

    CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.2, pp. 69-86, 2006, DOI:10.3970/cmes.2006.015.069

    Abstract In this paper we will study the numerical integrations of second order boundary value problems under the imposed conditions at t=0 and t=T in a general setting. We can construct a compact space shooting method for finding the unknown initial conditions. The key point is based on the construction of a one-step Lie group element G(u0,uT) and the establishment of a mid-point Lie group element G(r). Then, by imposing G(u0,uT) = G(r) we can search the missing initial conditions through an iterative solution of the weighting factor r ∈ (0,1). Numerical examples were examined to convince that the new approach… More >

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