Generation of Multivariate Hermite Interpolating Polynomials

1st Edition

Santiago Alves Tavares

Chapman and Hall/CRC
Published August 23, 2005
Reference - 704 Pages - 180 B/W Illustrations
ISBN 9781584885726 - CAT# C5726
Series: Chapman & Hall/CRC Pure and Applied Mathematics

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Features

  • Presents a fresh approach to the approximate solution of differential equations
  • Supplies algorithms and pseudocode for generating constrained numbers and Hermite interpolating polynomials
  • Contains detailed examples that clarify the algorithms and aid in troubleshooting the development of computer code
  • Demonstrates several applications of the algorithms, with both one-dimensional and multivariate examples
  • Summary

    Generation of Multivariate Hermite Interpolating Polynomials advances the study of approximate solutions to partial differential equations by presenting a novel approach that employs Hermite interpolating polynomials and bysupplying algorithms useful in applying this approach.

    Organized into three sections, the book begins with a thorough examination of constrained numbers, which form the basis for constructing interpolating polynomials. The author develops their geometric representation in coordinate systems in several dimensions and presents generating algorithms for each level number. He then discusses their applications in computing the derivative of the product of functions of several variables and in the construction of expression for n-dimensional natural numbers. Section II focuses on the construction of Hermite interpolating polynomials, from their characterizing properties and generating algorithms to a graphical analysis of their behavior.

    The final section of the book is dedicated to the application of Hermite interpolating polynomials to linear and nonlinear differential equations in one or several variables. Of particular interest is an example based on the author's thermal analysis of the space shuttle during reentry to the earth's atmosphere, wherein he uses the polynomials developed in the book to solve the heat transfer equations for the heating of the lower surface of the wing.

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