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.

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

part II|249 pages

Hermite Interpolating Polynomials

part III|123 pages

Selected applications