$**$Must be done on MatLab$**$

The Manning equation can be written for a rectangular open channel as

$Q=\frac{\sqrt[\phantom{2}]{S}(BH{)}^{\frac{5}{3}}}{n(B+2H{)}^{\frac{2}{3}}}$

where $Q=$ flow $(\frac{m^3}{s}),S=$ slope $(\frac{m}{m}),B=$ channel width $(m),H=$depth$(m),$ and $n=$ the

Manning roughness coefficient. Develop a fixed$-$point iteration scheme to solve this equation for

$H$ given $Q=10,S=0\mathrm{.}0001,B=30,$ and $n=0\mathrm{.}025.$ Show the your solutions in $10$ iterations, and

prove that your scheme converges for all initial guesses greater than or equal to zero. $[20$ pts$]$