Solving Nonlinear Equations Error
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I have a problem with solving two nonlinear equations using the newton method. My problem is that the code works with some values but with others I only receive the following errors:
??? Error using ==> erfc Input must be real and full.
Error in ==> normcdf at 94 p(todo) = 0.5 * erfc(-z ./ sqrt(2));
Error in ==> test4 at 14 f(1) = x*normcdf((log(x/18.5)+(0.005 +0.5*y^2))/y) - 18.5 * exp(-0.005)*normcdf((log(x/185)+(0.03 +0.5*y^2))/y)-y-0.5;
My Code is:
% Newton Raphson solution of two nonlinear algebraic equations
% set up the iteration
error1 = 1.e8;
xx(1) = 19.0; % initial guesses
xx(2) = 0.02;
iter=0;
itermax=3000.
% begin iteration
while error1>1.e-12
iter=iter+1;
x = xx(1);
y = xx(2);
% calculate the functions
f(1) = x*normcdf((log(x/18.5)+(0.005 +0.5*y^2))/y) - 18.5 * exp(-0.005)*normcdf((log(x/185)+(0.03 +0.5*y^2))/y)-y-0.5;
f(2) =(x/0.5)*normcdf((log(x/18.5)+(0.005 +0.5*y^2))/y)*y-1.42;
% calculate the Jacobian
J(1,1) = normcdf((log(x/18.5)+(0.005 +0.5*y^2))/y);
J(1,2) = x*1*(exp((-((log(x/18.5)+(0.005 +0.5*y^2))/y)^2)/2))/((sqrt(2)*pi*1)*x*y);
J(2,1) = normcdf((log(x/18.5)+(0.005 +0.5*y^2))/y)*y +(x*1*(exp((-((log(x/18.5)+(0.005 +0.5*y^2))/y)^2)/2))/((sqrt(2)*pi*1)*x*y));
J(2,2) = x*normcdf((log(x/18.5)+(0.005 +0.5*y^2))/y)+x*y*(exp((-((log(x/18.5)+(0.005 +0.5*y^2))/y)^2)/2))/((sqrt(2)*pi)*x*y)*((log(x/(18.5*exp(-0.005)))))/(y^2)+0.5;
% solve the linear equations
y = -J\f';
% move the solution, xx(k+1) - xx(k), to xx(k+1)
xx = xx + y';
% calculate norms
error1=sqrt(y(1)*y(1)+y(2)*y(2));
error(iter)=sqrt(f(1)*f(1)+f(2)*f(2));
ii(iter)=iter;
if (iter > itermax)
error1 = 0.;
s=sprintf('****Did not converge within %3.0f iterations.****',itermax);
disp(s)
end
% check if error1 < 1.e-12
end
x = xx(1);
y = xx(2);
f(1) = x*normcdf((log(x/18.5)+(0.005 +0.5*y^2))/y) - 18.5 * exp(-0.005)*normcdf((log(x/185)+(0.005 +0.5*y^2))/y)-y-0.5;
f(2) =(x/0.5)*normcdf((log(x/18.5)+(0.005 +0.5*y^2))/(y*1))*y-1.42;
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