Tavares Generation of Multivariate Hermite Interpolating Polynomials

Erscheinungsjahr 2010
ISBN: 978-1-4200-3485-1
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 704 Seiten

Reihe: Chapman & Hall/CRC Pure and Applied Mathematics

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.

Zielgruppe

Theoretical and applied mathematicians and students studying differential equations

Autoren/Hrsg.

Tavares, Santiago Alves

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

CONSTRAINED NUMBERS
Constrained Coordinate System
Generation of the Coordinate System
Natural Coordinates
Computation of the Number of Elements
An Ordering Relation
Application to Symbolic Computation of Derivatives

HERMITE INTERPOLATING POLYNOMIALS
Multivariate Hermite Interpolating Polynomial
Generation of the Hermite Interpolating Polynomials
Hermite Interpolating Polynomials: The Classical and Present Approaches
Normalized Symmetric Square Domain
Rectangular Nonsymmetric Domain
Generic Domains
Extensions of the Constrained Numbers
Field of the Complex Numbers
Analysis of the Behavior of the Hermite Interpolating Polynomials

SELECTED APPLICATIONS
Construction of the Approximate Solution
One-Dimensional Two-Point Boundary Value Problems
Application to Problems with Several Variables
Thermal Analysis of the Surface of the Space Shuttle
References
Index