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Two methods for developing high order single step explicit algorithms on symmetric stencils with data on only one time level are presented. Examples are given for the convection and linearized Euler equations with up to the eighth order accuracy in both space and time in one space dimension, and up to the sixth in two space dimensions. The method of characteristics is generalized to nondiagonalizable hyperbolic systems by using exact local polynominal solutions of the system, and the resulting exact propagator methods automatically incorporate the correct multidimensional wave propagation dynamics. Multivariate Taylor or Cauchy-Kowaleskaya expansions are also used to develop algorithms. Both of these methods can be applied to obtain algorithms of arbitrarily high order for hyperbolic systems in multiple space dimensions. Cross derivatives are included in the local approximations used to develop the algorithms in this paper in order to obtain high order accuracy, and improved isotropy and stability. Efficiency in meeting global error bounds is an important criterion for evaluating algorithms, and the higher order algorithms are shown to be up to several orders of magnitude more efficient even though they are more complex. Stable high order boundary conditions for the linearized Euler equations are developed in one space dimension, and demonstrated in two space dimensions.

1Life of Benjamin Franklin

By Samuel G Goodrich

<p>This little book was intended for the education of school children and includes tales, sketches and anecdotes of his life written for the children of the mid 1800's and written in the English language of that period. Each chapter has numerous questions intended for the the reader or the teacher to quiz themselves to see if they gathered the pertinent information. The quiz questions will not be recorded. Also part of this book are numerous short essays written by Franklin on various topics. These entertaining and insightful samples occupy sections 17 through 27. (Summary by phil chenevert)

2Poems

By Samuel G Goodrich

This is a very varied collection of poems by Samuel G. Goodrich, alias Peter Parley. Some of the poems in this volume are rather dark and somber, others of a more light-hearted tone. Some of the poems are addressed to children, some are better enjoyed by adults. In any case, each reader, or listener, should find something suited to his or her tastes and moods in this collection. - Summary by Carolin

3Great Events in the History of North and South America

By Charles Goodrich

Step back and time and learn about people, places, and things that helped to mold North and South America. - Summary by CBTeddy