Using the Taylor series expansion, the following centered finite difference approximation of the first derivative can be derived and it can be proven that the errors are second order of the step size: f'(x) = (f(x h) - f(x-h))/(2h)The following forward-difference approximation of the second derivative can be derived:f”(x) = (f(x h) - 2f(x) f(x-h))/h^2A higher accurate forward-difference approximation of the first derivative can be derived as:f'(x) = (-f(x 2h) 4f(x h) - 3f(x))/(2h)Numerical d
Using the Taylor series expansion, the following centered finite differ…
Feb 7, 2022
numerade.com
SOLVED: NUMERICAL METHODS (Computing Finite-Difference Formulas for Derivatives). Use a Taylor series expansion to derive a centered finite-difference approximation to the third derivative that is second-order accurate. Hint: you will have to use four different expansions for the points xi-2, xi-1, xi 1, and xi 2. In each case, the expansion will be around the point xi. The interval ∆x will be used in each case of i - 1 and i 1, and 2∆x will be used in each case of i - 2 and i 2. The fou
SOLVED: NUMERICAL METHODS (Computing Finite-Difference For…
1 month ago
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SOLVED:The objective of this problem is to compare second-order accurate forward, backward, and centered finite-difference approximations of the first derivative of a function to the actual value of the derivative. This will be done for f(x)=e^-2 x-x (a) Use calculus to determine the correct value of the derivative at x=2. (b) To evaluate the centered finite-difference approximations, start with x=0.5 . Thus, for the first evaluation, the x values for the centered difference approximation will b
SOLVED:The objective of this problem is to compare second-ord…
May 12, 2020
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Solve problem 2.7 using a second-order accurate central differe... | Filo
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