5. Consider the folowing table
| x | -1 | -0.5 | 0 | 0.5 | 1 |
|------|-----|------|----|-----|----|
| f(x) | 15 | 10 | 14 | 13 | 20 |
The second derivative f''(0) is estimated using:
(a) Using 3pt-CFD.
(b) Using 3pt-BFD.
(c) Using 3pt-FFD.
Which result is third order? Circle the right answer
a. None of them
b. (b)
c. (a)
d. (c)
6. Consider the ODE
$$y'=xy+1$$
$$y(0) = 2$$
Estimate the solution y(x) at x = 0.4 (this means we need to estimate y(0.4)) using Euler explicit with an
accuracy of 0.2. tick the right (or very close) answer
a. y(0.4) ≈ 2.210
b. y(0.4) ≈ 5.2
c. y(0.4) ≈ 2.488
d. y(0.4) ≈ -3.36
7. We need to solve numerically using Euler implicit the equation
$$y'=y-xy+1$$
$$y(0) = 3$$
for x ∈ [0,6] with N = 31 points
Find h then calculate the estimates y₂. tick the right (or very close) answer
a. y₂ = -4.68
b. y₂ = 3
c. y₂ = 4.56
d. y₂ = 3.809
8. The firstt derivative f '(0.9) of the function f(x) = e^(x^2) is estimated using
(a) 2pt FFD with a given h
(b) 2pt-CFD with 10h
What is the value of h to get the same accuracy? Circle the right answer.
a. 1.610^-3
b. 10^-2
c. 10
d. No h can make both accuracies equal
9. We need to solve numerically using Euler explicit the equation
$$y'= y^2 - xy + 1$$
$$y(0) = 3$$
for x ∈ [0,6] with h = 0.2
Calculate the estimates y₂. circle the right (or very close) answer
a. y2 = 8.25
b. y2 = 5
c. y₂ = 1.54
d. y₂ = 10