Thread: Newton Method, to solve nonlinear equations, in Matlab

I have a set of nonlinear equations. And it was proved to have a unique solution. But I can't get the result by using matlab. I thought matlab is using Newton Method. Does anybody know what's wrong about this application?

Originally Posted by unsown

I have a set of nonlinear equations. And it was proved to have a unique solution. But I can't get the result by using matlab. I thought matlab is using Newton Method. Does anybody know what's wrong about this application?

Show us what you are trying to do/have done. Otherwise we are just guessing

.

I also have a similar problem and I am having trouble writing a matlab program to solve it. My program so far is as follows:

Code:

m=2.0;
P=4.0;
Q=5.0;

f=@(x,y) y-((1/m)*((exp(x/m))+(exp(-x/m))));
g=@(x,y) ((x^2)/(P^2))+((y^2)/(Q^2))-1;

fd1=@(x,y) (1/(m^2))*((exp(x/m))-(exp(-x/m)));
fd2=@(x,y) 1;

gd1=@(x,y) ((2*x)/(P^2));
gd2=@(x,y) ((2*y)/(Q^2));

i=1;
N=100;
TOL=0.001;
x=1;
y=1; 

while i<N
   A=[fd1 fd2; gd1 gd2];

I know it is far from complete but any advice or suggestions would be very much appreciated.

You have the sign of df/dx wrong.

The following works:

Code:

m=2.0;
P=4.0;
Q=5.0;
 
 
f=@(x,y) y-(1/m)*(exp(x/m)+exp(-x/m));
g=@(x,y) (x^2)/(P^2)+(y^2)/(Q^2)-1;
 
 
fd1=@(x,y) -(1/(m^2))*(exp(x/m)-exp(-x/m));
fd2=@(x,y) 1;
 
gd1=@(x,y) (2*x)/(P^2);
gd2=@(x,y) (2*y)/(Q^2);
 
 
TOL=0.001;
x=-1;
y=-1;
xx=zeros(2,1);
 
err=100;
 
 
while err>TOL
    J=[fd1(x,y) fd2(x,y); gd1(x,y) gd2(x,y)];
 
    xx=[x;y];
    xx=xx-inv(J)*[f(x,y);g(x,y)];  %xx=xx-J\[f(x,y);g(x,y)] would be better
    x1=xx(1);y1=xx(2);
    err=sqrt((x-x1)^2+(y-y1)^2);
    x=x1;y=y1;
end
 
xx

CB

Thank you for that bit of code. I really appreciate the help.