Section 4.1 Numerical Differentiation
www3.nd.edu › ~zxu2 › acms40390F15Example 4.4.1 Use forward difference formula with β= 0.1 to approximate the derivative of ππ (π₯π₯) = ln(π₯π₯) at π₯π₯0= 1.8. Determine the bound of the approximation error. Forward-difference: ππ′(π₯π₯ 0) ≈ ππ(π₯π₯0+β)−ππ(π₯π₯0) β when β> 0. Backward-difference: ππ′(π₯π₯ 0) ≈
5 Numerical Diο¬erentiation
www2.math.umd.edu › lecture-notes › differentiation-chapan exact formula of the form f0(x) = f(x+h)−f(x) h − h 2 f00(ξ), ξ ∈ (x,x+h). (5.3) Since this approximation of the derivative at x is based on the values of the function at x and x + h, the approximation (5.1) is called a forward diο¬erencing or one-sided diο¬erencing. The approximation of the derivative at x that is based on the values of