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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Generation of Multivariate Hermite Interpolating Polynomials (Paperback)
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Generation of Multivariate Hermite Interpolating Polynomials (Paperback)
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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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