Numerical Differentiation -- from Wolfram MathWorld
mathworld.wolfram.com › NumericalDifferentiationDec 17, 2021 · Numerical differentiation is the process of finding the numerical value of a derivative of a given function at a given point. In general, numerical differentiation is more difficult than numerical integration. This is because while numerical integration requires only good continuity properties of the function being integrated, numerical differentiation requires more complicated properties such as Lipschitz classes.
Numerical Differentiation - University of Utah
my.mech.utah.edu › ~pardyjak › me2040Numerical Differentiation Now, keep the f’’ term and write a forward TS about xi+2 Multiply (1) by 2 and subtract from (3): + = + + +⋅⋅ 2 ''( )4 ( ) ( ) '( )2 2 2 f x h f x f x f x h i i i i (3) 2 − 2f(xi+1)=2f(xi)+2f'(xi)h+f''(xi)h 2 f(xi+2)=f(xi)+2f'(xi)h+2f''(xi)h 2 f(xi+2)−2f(xi+1)=−f(xi)+f''(xi)h ( ) 2 ( ) ( ) ''( ) 2 2 1 O h h f x f x f x f x i i i i +
5 Numerical Differentiation
www2.math.umd.edu › lecture-notes › differentiation-chapThe numerical differentiation formula, (5.9), then becomes f0(x k) = Xn j=0 f(x j)l0 j (x k)+ 1 (n+1)! f(n+1)(ξ x k) Y j=0 j6= k (x k −x j). (5.10) We refer to the formula (5.10) as a differentiation by interpolation algorithm. Example 5.1 We demonstrate how to use the differentiation by integration formula (5.10) in the case where n = 1 and k = 0.