Generation of Multivariate Hermite Interpolating Polynomials

This text advances the study of approximate solutions to partial differential equations by formulating a novel approach that employs Hermite interpolating polynomials and by supplying algorithms useful in applying this approach. The book''s three sections examine constrained numbers, Hermite interpolating polynomials, and selected applications. The authors outline the rules for writing the algorithms and then present them in pseudo-code. Next, they define the properties that characterize the Hermite interpolating polynomials, propose an expression and demonstrate an algorithm for generating the polynomials, and show the advantages of this new technique over the classical approach.

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.