## Numerical Analysis: A.R. Mitchell 75th Birthday VolumeThis volume is intended to mark the 75th birthday of A R Mitchell, of the University of Dundee. It consists of a collection of articles written by numerical analysts having links with Ron Mitchell, as colleagues, collaborators, former students, or as visitors to Dundee. Ron Mitchell is known for his books and articles contributing to the numerical analysis of partial differential equations; he has also made major contributions to the development of numerical analysis in the UK and abroad, and his many human qualitites are such that he is held in high regard and looked on with great affection by the numerical analysis community. The list of contributors is evidence of the esteem in which he is held, and of the way in which his influence has spread through his former students and fellow workers. In addition to contributions relevant to his own specialist subjects, there are also papers on a wide range of subjects in numerical analysis. |

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### Contents

The Finite Element Method and Computer Aided | 9 |

RuggeKutta Methods as Mathematical Objects | 39 |

RungeKutta Methods on Manifolds | 57 |

Numerical Solutions of One and Two Dimensional Hyperbolic | 71 |

Numerical Experiments for a Nonoverlapping Domain | 85 |

A Piecewise Uniform Adaptive Grid Algorithm for Nonlinear | 99 |

Diagonal Dominance and Positive Definiteness of Upwind | 125 |

Chaos in Numerics | 133 |

A TwoStep Iterative Method | 177 |

A Method of Lines Package Based on Monomial Spline Collocation | 207 |

Solving Least Squares Problems on Parallel Vector Processors | 225 |

Aspects of MEstimation and i Fitting Problems | 247 |

On Generalized Bernstein Polynomials | 263 |

A Generalized Discrete Multiple Scales Analysis Technique | 291 |

Numerical Solution of Burgers Equation using a TwoGrid | 305 |

Exact Difference Formulas for Linear Differential Operators | 155 |

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