Abstract
This paper treats the nonlinear, two-point boundary-value problem formulated by Troesch (Ref. 3) and studied by Roberts and Shipman (Ref. 4). Computationally speaking, this is a difficult problem, owing to the fact that the Jacobian matrix is characterized by large positive eigenvalues. The resulting numerical difficulties are reduced by treating the two-point boundary-value problem as a multipoint boundary-value problem. The modified quasilinearization algorithm of Refs. 5–6 is employed. This approach bypasses the integration of the nonlinear equations, which characterizes shooting methods. Computational results are also presented for another difficult nonlinear, two-point boundary-value problem, namely, the problem formulated by Holt (Ref. 7).
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