Nonlinear Equation solution of one variable ?

Ammar Ahmed

2019 10 16

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I'm trying to solve this modified effective permittivity non linear equation using newton raphson method, the solution does not return a pair of complex solution, could anyone help me with coding!

p=[0.23]
er1=(10000); % first relative permttivity 
er2=(2.5); % second relative permttivity 
Hc=(10^6); 
H=[0,2.5*10^4,5.0*10^4,7.5*10^4,1*10^5,1.3*10^5,1.5.*10^5];
Pc=(0.33).*exp(-abs(H)/Hc);
c1=(1-3*Pc).*(((p)./(Pc)).^Pc).*(((1-p)./(1-Pc)).^(1-Pc)); %concnetration 
% wanted solution for varaible x 
f=@(x) ((p.*(x-er1)./(er1-2.*x))./(1+c1.*(x-er1)./(er1-2.*x))+((1-p).*(x-er2)./(er2-2.*x))./(1+c1.*(x-er2)./(er2-2.*x))); %Equation 4
df=@(x) ((3.*er1.*p)./(er1+2.*x+c1.*(x-er1)).^2)+(((x-er2).*(1-p))./(er1+2.*x+c1.*(x-er1)));  %derivative of the above function
 a=1; b=20; 
 x=a;
 for i=1:1:100
 x1=x-(f(x)/df(x));
 x=x1;
 end
 sol=x;
 fprintf('Approximate Root is %.15f',sol)
 a=1;b=20; 
 x=a;
 er(5)=0;
 for i=1:1:5
 x1=x-(f(x)/df(x));
 x=x1;
 er(i)=x1-sol;
 end
 plot(er)
 xlabel('Number of iterations')
 ylabel('Error')
 title('Error Vs. Number of iterations')