Generation of Multivariate Hermite Interpolating PolynomialsThis 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. |
Contents
3 | |
Generation of the coordinate system | 31 |
Natural coordinates | 113 |
Computation of the number of elements | 135 |
An ordering relation | 185 |
Application to symbolic computation of derivatives | 217 |
Hermite Interpolating Polynomials | 285 |
Multivariate Hermite Interpolating Polynomial | 287 |
Generic domains | 467 |
Extensions of the constrained numbers | 481 |
Field of the complex numbers | 487 |
Analysis of the behavior of the Hermite Interpolating Polynomials | 499 |
Selected applications | 535 |
Construction of the approximate solution | 537 |
Onedimensional twopoint boundary value problems | 551 |
Application to problems with several variables | 603 |
Generation of the Hermite Interpolating Polynomials | 335 |
Hermite Interpolating Polynomials the classical and present approaches | 339 |
Normalized symmetric square domain | 355 |
Rectangular nonsymmetric domain | 433 |
Thermal analysis of the surface of the space shuttle | 617 |
659 | |
663 | |
Other editions - View all
Generation of Multivariate Hermite Interpolating Polynomials Santiago Alves Tavares Limited preview - 2005 |
Generation of Multivariate Hermite Interpolating Polynomials Santiago Alves Tavares No preview available - 2019 |
Generation of Multivariate Hermite Interpolating Polynomials Santiago Alves Tavares No preview available - 2005 |
Common terms and phrases
1.00 normalized coordinate Analysis approximate solution axis basis boundary conditions cartesian product Chapter Chebyshev polynomial coefficients Computation considered constant constrained numbers constrained space Construction contains coordinate axes coordinate numbers corresponding defined definition derivative of order differential equation domain end of example equals error evaluated exact solution expansion exponents expression factor follows Geometric representation given by equation gives Graphic Hermite Interpolating Polynomials indices layer level Ao(v loop node a0 norm number of elements obtained obtained in equation one-dimensional order of derivative origin performed permutation polynomials related power series problem reference node region represented residual respect rules satisfy shown in figure shows solved sublevel subset Substituting Table temperature theorem transformation triangle two-dimensional underlying set underlying set Z+ union variables writes written zero zero-dimensional