Using the newtmultm MATLAB function determine the solution o

Using the newtmult.m MATLAB function, determine the solution of the simultaneous nonlinear equations:

Use initial guesses x1=1.5, x2=1.5

x1^2 = 5 – x2^2

x2^2 + 1 = x1^2

Solution

matlab function:

[x,f,ea,iter]=newtmult(func,x0,es,maxit,p1,p2,...):
% uses the Newton-Raphson method to find the roots of
% a system of nonlinear equations
% input:
% func = name of function that returns f and J
% x0 = initial guess
% es = desired percent relative error (default = 0.0001%)
% maxit = maximum allowable iterations (default = 50)
% p1,p2,... = additional parameters used by function
% output:
% x = vector of roots
% f = vector of functions evaluated at roots
% ea = approximate percent relative error (%)
% iter = number of iterations

if nargin<2,error(\'at least 2 input arguments required\'),end
if nargin<3|isempty(es),es=0.0001;end
if nargin<4|isempty(maxit),maxit=50;end
iter = 0;
x=x0;
while (1)
[J,f]=func(x,varargin{:});
dx=J\\f;
x=x-dx;
iter = iter + 1;
ea=100*max(abs(dx./x));
if iter>=maxit|ea<=es, break, end
end