Bisectional Method and Newton-Raphson Method

The volume of liquid (V) in a hollow horizontal cylinder of radius r and length L is related to the depth of the liquid h by

V=(r^2 〖cos〗^(-1) ((r-h)/r)-(r-h) √(2rh-h^2 ))L

Determine h given r = 2.0 m, L = 5.0 m, and V = 8.0 m3.

Perform the computation until the relative error is less than 0.05%.

For the Bisection use hl = 1.0 m (lower limit) and hu = 2.0 m. (upper Limit). For the

Newtow-Raphson and Secant methods use an initial value of h=1.0 or h=2.0 m.

• By using the Bisection Method first (20pts)
• then, do the same, by using the Newton-Raphson method, (40pts)
• also, do the same using the Secant Method (30pts) and finally,
• compare the speed of these methods by using Matlab (tic and toc command) or Python (the time library) and discuss your results (10pts)

[Adam Syer]

please can someone help