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.

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

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