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**Implementation issues in solving nonlinear equations for two-point boundary value problems.**
*(English)*
Zbl 0721.65043

Complex numerical methods often contain subproblems that are easy to state in mathematical form, but difficult to translate into software. Several algorithmic issues of this nature arise in implementing a Newton iteration scheme as part of a finite-difference method for two-point boundary value problems. We describe the practical as well as theoretical considerations behind the decisions included in the final code, with special emphasis on two “watchdog” strategies designed to improve reliability and allow early termination of the Newton iterates.

Reviewer: J.R.Cash

### MSC:

65L10 | Numerical solution of boundary value problems involving ordinary differential equations |

65L12 | Finite difference and finite volume methods for ordinary differential equations |

34-04 | Software, source code, etc. for problems pertaining to ordinary differential equations |

34B15 | Nonlinear boundary value problems for ordinary differential equations |

### Keywords:

nonlinear algebraic equations; merit functions; mathematical software; watchdog strategy; Newton iteration scheme; finite-difference method
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\textit{J. R. Cash} and \textit{M. H. Wright}, Computing 45, No. 1, 17--37 (1990; Zbl 0721.65043)

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### References:

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