Newton Raphson on MATLAB

Question

Türker Demiröz 2021-2-19

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/750714-newton-raphson-on-matlab

回答： Jemima Pulipati 2021-2-23

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