ABSTRACT
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.
TABLE OF CONTENTS
part I|284 pages
Constrained Numbers
chapter Chapter 1|28 pages
Constrained coordinate system
chapter Chapter 2|82 pages
Generation of the coordinate system
chapter Chapter 3|22 pages
Natural coordinates
chapter Chapter 4|50 pages
Computation of the number of elements
chapter Chapter 5|32 pages
An ordering relation
chapter Chapter 6|68 pages
Application to symbolic computation of derivatives
part II|249 pages
Hermite Interpolating Polynomials
chapter Chapter 7|48 pages
Multivariate Hermite Interpolating Polynomial
chapter Chapter 8|4 pages
Generation of the Hermite Interpolating Polynomials
chapter Chapter 9|16 pages
Hermite Interpolating Polynomials: the classical and present approaches
chapter Chapter 10|78 pages
Normalized symmetric square domain
chapter Chapter 11|34 pages
Rectangular nonsymmetric domain
chapter Chapter 12|13 pages
Generic domains
chapter Chapter 13|5 pages
Extensions of the constrained numbers
chapter Chapter 14|12 pages
Field of the complex numbers
chapter Chapter 15|35 pages
Analysis of the behavior of the Hermite Interpolating Polynomials
part III|123 pages
Selected applications