Newton Jacobi Nonlinear System

clear;

x(1)=2;

y(1)=1;

z(1)=2;

for k=1:100

F(1,1)= x(k)^2* y(k)+x(1)^0.5*y(1)^2-z(k);

F(2,1)= exp(x(k))-z(k)^2-sin(y(1));

F(3,1)= x(k)*y(k)*z(k)-x(k)-y(k)-z(k);

J(1,1:3)= [2*x(k)*y(k)-1/(2*x(k)^0.5), x(k)^2+2*x(k)^0.5*y(k), -1];

J(2,1:3)= [exp(x(k)), -cos(y(k)), -2*z(k)];

J(3,1:3)= [y(k)*z(k)-1, x(k)*z(k)-1, x(k)*y(k)-1];

X= [x(k);y(k);z(k)];

Xnew= X-J^-1*F;

x(k+1)=Xnew(1);

y(k+1)=Xnew(2);

z(k+1)=Xnew(3);

xerr= abs(x(k+1)-x(k));

yerr= abs(y(k+1)-y(k));

zerr= abs(z(k+1)-z(k));

e(k+1)= max(xerr,yerr,zerr);

if e(k+1)<0.0001

break; end

end

[x' y' z' e']

Error using max

Dimension argument is not supported when two input arrays are provided.

Answer 1

[Alan Stevens]

Replace

e(k+1)= max(xerr,yerr,zerr);

with

e(k+1)= max(max(xerr,yerr),zerr);