August 2024
Intermediate to advanced
355 pages
11h 19m
English
Content preview from Zhang Time Discretization (ZTD) Formulas and Applications
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Chapter 16Lagrange Numerical-Differentiation Formulas
Abstract
In order to achieve higher computational precision in approximating the first-order derivative of the target point, Lagrange numerical-differentiation formulas (also known as one-step-ahead numerical-differentiation formulas) are presented. These formulas greatly remedy some intrinsic weaknesses of backward numerical-differentiation formulas and overcome limitation of central numerical-differentiation formulas. In addition, a group of formulas are proposed to obtain the optimal sampling gaps. Moreover, the error analyses of Lagrange numerical-differentiation formulas and backward numerical-differentiation formulas are further investigated. Numerical ...
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