Newton Raphson on MATLAB

Hello Community. Here im trying to find the rho_a using the Newton Raphson Method. But im new to MATLAB and can't figure it out by myself.

Here's my Code;

clc; clear all
f_o =0.527; 
f_i = 0.506;      
Z = 8;               
D_w = 10.32;            
rho_0 = (f_i+f_o-1)*D_w;      
F_a =2600;
alpha_no = 7.61;
C_delta = 7.14*10^5;
LHS=F_a/(Z*C_delta*rho_0^3/2);
syms rho_a
f = @(rho_a) ((sin(alpha_no)+rho_a)/((cos(alpha_no)^2+(sin(alpha_no)+rho_a)^2))^1/2)*(((cos(alpha_no)^2+(sin(alpha_no)+rho_a)^2))^1/2)-1^3/2;
fd = diff(f(rho_a));
rho_a = 10^-6;

for i=1:100000
    rho_a = rho_a - f./fd;
    f=rho_a;
  if abs(f-LHS/LHS)<=10^-4
break
  end
  
end

Answer 1

[Jemima Pulipati]

Hello,

From my understanding, you want to implement the Newton Raphson method in MATLAB.

The following answer from the community might be of relevance to you.

https://www.mathworks.com/matlabcentral/answers/107508-solving-a-nonlinear-equation-using-newton-raphson-method

The following file exchange submission might also help you.

https://www.mathworks.com/matlabcentral/fileexchange/73563-newton-raphson-method