how to solve multiple iteration for multiple input?

I want to solve this equation ∆ε=∆σ/E+2(∆σ/2k)^n for ∆σ using iteration. I have ε ranging from (0 to 2).

• ∆ε is elongation
• ∆σ is stress
• E is modulus of elasticity
• K and n are constant

x = 16; %x is ∆σ
x_old = 100;
iter = 0;
k=38.177;
n=7.22;
E=15.25;
% y=linspace(0,5,0.5);
for i=[0:.01:0.5]
  while abs(x_old-x) > 10^-3 && x ~= 0
      x_old = x;
      x = x - (2*(x/(2*k))^(n) + (x/(E))-i)/(2*n*(x/(2*k))^(n-1) + (1/(E)));
      iter = iter + 1;
      fprintf('Iteration %d: x=%.20f\n', iter, x);
      pause;
  end
end

I have script for Newton-Raphson Method for finding out ∆σ, but i don't know know how solve for multiple values. what i mean by multiple value is i have different ∆ε, ranging from 0 to 2. once i solved the iteration, i want to plot it as well. I think i could figure out ploting, but it would be helpful, if you could guide me on this. thank you very much!

sincerely siva

Answer 1

[Abhi Sundararaman]

You could create another for loop outside your "while" loop that changes epsilon during each iteration. Then you substitute this value of epsilon into your iteration equation inside your while loop. For example,after initializing your constants,

x = 16; %guess for x
Epsilon = 0:0.1:2
Sigma = zeros(size(Epsilon));
i = 1;
for Epsilon = 0:0.1:2
  x = 16; %reinitialize the guess for x
 while  abs(x_old - x) > 10^-3 && x ~= 0
    <insert your iteration equation here, with Epsilon included>
    <solve for sigma (x)>
 end
 Sigma(i) = x;
 i = i + 1;
end
plot( Epsilon, Sigma );