Layered model:

Natural language | (description in words - ambiguous, the most general) |

Mathematical abstraction | (equations, strict conditions, unambiguous, less general) |

Numerical Method | (solve equations numerically, works in certain
cases, numerical stability, suitable for parallel implementation?) No Free Lunch theorem www.no-free-lunch.org |

Numerical Algorithm | (Implementation, modular design, pseudo-code/flow chart) |

Program | (programming language, implementation, compilation, debugging, platforms, documentation, stability and security concerns) |

Solutions | (test, nontrivial examples, run time) |

Presentation |
(output data representation, snapshots, packaging, advertising, website) |

Natural language: Precisely calculate π.

Mathematical abstraction:

Numerical Method:

Find the root of the function:

Possible Numerical Methods:

a. Interval splitting

b. Fixed-point method

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