Post by matthorr on Sept 10, 2015 17:40:23 GMT
Consider the following periodic function:
\( u(x) = \sum_{k=1}^6 \frac{1}{k} \sin(2kx) \)
Please plot the exact function on one figure for 0 < x < 2π. What do you think the function would look like if the summation was not stopped with 6 terms but rather had an infinite number of terms (just include a sketch)? Derive the exact first derivative and plot on a second figure. What do you think the first derivative of the function would look like if the summation was not stopped with 6 terms but rather had an infinite number of terms (sketch)? Use a three point central difference to approximate the first derivative for the given periodic function at x = π/8 with Δx = 0.04 and Δx = 0.02 and compare to the exact solution. What are the errors for both of these approximations? Any comments?
\( u(x) = \sum_{k=1}^6 \frac{1}{k} \sin(2kx) \)
Please plot the exact function on one figure for 0 < x < 2π. What do you think the function would look like if the summation was not stopped with 6 terms but rather had an infinite number of terms (just include a sketch)? Derive the exact first derivative and plot on a second figure. What do you think the first derivative of the function would look like if the summation was not stopped with 6 terms but rather had an infinite number of terms (sketch)? Use a three point central difference to approximate the first derivative for the given periodic function at x = π/8 with Δx = 0.04 and Δx = 0.02 and compare to the exact solution. What are the errors for both of these approximations? Any comments?
