Question

Write a function named “NewtonRaphson” that implements the Newton-Raphson method. The inputs to this function are the name of the function, name of the function’s derivative function, initial guess, maximum number of iterations, and tolerance for the relative convergence error. The output is the root. Use the problem in Homework #3 to test your function.   

Hw 3 that we are pulling from

%Newton-Raphson method to find upward velocity of a rocket
clear all;
clc;
u=2200; %m/s
m0=160000; %kg
q=2680; %kg/s
g=9.81; %m/s^2
e=1; %Starting error
t=(0:1:50);
x0=25;%initial guess
f=u*log(m0./(m0-(q*x0)))-g*x0-1000; %Given Function
fd=(q*u)./((m0-q.*x0)-g);
plot(t,f) %Used to determine x0 valuebelow
while e>10^(-8)
xi=x0-(f/fd);
e=abs((xi-x0)/xi)*100;
if e<=10^(-8)
root=xi;
break
else
x0=xi;
end
f=u*log(m0./(m0-(q*x0)))-g*x0-1000;
fd=(q*u)./((m0-q.*x0)-g);
end
disp('Time when v=1000 m/s is')
disp(xi)

  

Answer 1

function r = NewtonRaphson(f, df,x0,N,tol)
x=x0;
for i = 1:N
xl=x;
x = xl - f(xl)/df(xl);
if (abs(x - xl)/x) < tol
r = xl;
break
end
end
end