Newton-Raphson Method for Non-linear System of 3 variables in Matlab
2 visualizaciones (últimos 30 días)
Mostrar comentarios más antiguos
dave
el 17 de Jun. de 2014
Comentada: Ankit Barthwal
el 23 de Mayo de 2017
I am trying to solve 3 non-linear system of 3 variables using the newton-raphson method in matlab. Here are the 3 non-linear equations:
c[alpha I+ k_f+k_d+k_ns+k_p(1-q)]-I alpha =0
s[lambda_b c P_C +lambda_r (1-q)]- lambda_b c P_C =0
q[gamma +c k_p (P_C/P_Q)]- c k_p (P_C/P_Q)=0
I need to find the values of c,s, and q using the newton-raphson method.
=> can someone please check my code, there are no errors so, its converges after six iterations. can give the accurate values of c,s and q.
I am only concern about this line in my matlab code:
disp(sprintf('iter=%6.15f, c=%6.15f, s=%6.15f, q=%6.15f', iter,xnew));
I want to display xnew as new and accurate values for c,s and q. Is this code giving the correct and update values of c,s,q as xnew? Sorry if my question looks silly. Thanks in advance.
This is my matlab code :
format long
clear;
%values of parameters
I=1200;
k_f= 6.7*10.^7;
k_d= 6.03*10.^8;
k_n=2.92*10.^9;
k_p=4.94*10.^9;
lambda_b= 0.0087;
lambda_r =835;
gamma =2.74;
alpha =1.14437*10.^-3;
P_C= 3 * 10.^(11);
P_Q= 2.87 * 10.^(10);
tol = 10.^-4; %tol is a converge tolerance
%initial guess or values
c=1;
s=0.015;
q=0.98;
iter= 0; %iterations
xnew =[c;s;q];
xold = zeros(size(xnew));
while norm(xnew - xold) > tol
iter= iter + 1;
xold = xnew;
% update c, s, and q
c = xold(1);
s = xold(2);
q = xold(3);
%Defining the functions for c,s and q.
f = c * (alpha*I + k_f + k_d + k_n * s + k_p*(1-q))-I *alpha;
g = s * (lambda_b * c* P_C + lambda_r *(1-q))- lambda_b* c * P_C;
h = q * ( gamma + c * k_p *(P_C / P_Q))- (c * k_p * (P_C / P_Q));
%Partial derivatives in terms of c,s and q.
dfdc = alpha*I + k_f + k_d + k_n * s + k_p*(1-q);
dfds = k_n *c ;
dfdq = - k_p *c;
dgdc = lambda_b * P_C *(s-1);
dgds = lambda_b * c* P_C + lambda_r *(1-q);
dgdq = - lambda_r * s;
dhdc = k_p *(P_C / P_Q)*(q-1);
dhds = 0;
dhdq = gamma + c * k_p *(P_C / P_Q);
%Jacobian matrix
J = [dfdc dfds dfdq; dgdc dgds dgdq; dhdc dhds dhdq];
% Applying the Newton-Raphson method
xnew = xold - J\[f;g;h];
disp(sprintf('iter=%6.15f, c=%6.15f, s=%6.15f, q=%6.15f', iter,xnew));
end
0 comentarios
Respuesta aceptada
Roger Stafford
el 17 de Jun. de 2014
I do see an error in your code, though it does not account for why you get only one iteration. You are not renewing the value of x0 inside the while-loop and therefore it continues to be the original estimate values. Also you are not renewing the values of c, s, and q from your 'xnew' values. The way the code reads, if it repeats for a second iteration, the while-loop should run forever, since nothing is ever changed after that.
4 comentarios
Ankit Barthwal
el 23 de Mayo de 2017
can you please send the code after corrections, I have to solve 3 non-linear equations as well.
Más respuestas (0)
Ver también
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!