a. An alternative derivation of FEFD is to equate the approximate slope (V,) of the approximate...

 

Transcribed Image Text:

a. An alternative derivation of FEFD is to equate the approximate slope (V,) of the approximate solution (curve) y(x) to the chord connecting the leading and trailing edges over the cell of interval (h =x+1-x,) on the curve. Show that this leads to the FEFD approximation to the ODE Y'(x) = /(x,Y (x)) b. Apply the same concept as in (a) but at the center of the interval X/2 =x, +h/2 to derive the midpoint rule FEFD called FEFDMP y, = Y-+hf (x/2:Ya/2), where Yasu2 y(x, +h/2). a. An alternative derivation of FEFD is to equate the approximate slope (V,) of the approximate solution (curve) y(x) to the chord connecting the leading and trailing edges over the cell of interval (h =x+1-x,) on the curve. Show that this leads to the FEFD approximation to the ODE Y'(x) = /(x,Y (x)) b. Apply the same concept as in (a) but at the center of the interval X/2 =x, +h/2 to derive the midpoint rule FEFD called FEFDMP y, = Y-+hf (x/2:Ya/2), where Yasu2 y(x, +h/2).

Answer rating: 100% (QA)

20 4a An alternative derivation of FEFD is to equate the approximate slope 1 of the appr... View the full answer