Moreover, our method provides us with the smooth solution in the form of Taylor polynomial
Transform the truth membership, indeterminacy membership, falsity membership functions by using first-order Taylor polynomial
The simplistic one uses the Taylor polynomial
related to the function defining the equation, considered at the previous iteration.
Errors and their bounds of the Taylor polynomial
approximation are shown in Fig.
In such a case, the Taylor's theorem ensures that the remainder term e, that is the approximation error given by the difference between the real value attained by the function and its Taylor polynomial
, is negligible if compared to the size of [(x - a).
Approximate solution for nonlinear Volterra-Fredholm integral equation by using Taylor polynomial
was given by Yalcinbas, 2002.
Four examples are presented to illustrate the approach which include the order verification of the errors in Taylor polynomial
approximation, the 5-point forward numerical differentiation formula, the composite Simpson method, and the 4-stage explicit Runge-Kutta method.
Ironically it is the Taylor polynomial
that is (in the language of algebra) the remainder of the division, while the "remainder" in Taylor Theorem is the main part.
It determines the order of Taylor polynomial
(8) and the higher it is, the more accurate the approximation [s.
For each [member of] N the Taylor polynomial
of the function f is defined as
The authors provide a precalculus review before covering limits, differentiations, the applications of the derivative, the integral, applications of the integral, techniques of integration, advanced applications of the integral and Taylor polynomials
, differential equations, infinite series, parametric equations, polar coordinates, and conic sections over the bookAEs eleven chapters.
Approximation Theory: From Taylor Polynomials
to Wavelets", Birkhauser, Boston, 2004.