clc;clear;close all
% define the function as anonymous
f = @(x,t) [460.*cos(x).*t+210.6.*t-25082;460.*sin(x).*t-6248]; % x = theta
theta_0 =0;% Initial guess for Theta
t_0 = 1; % Inital guess for t
es = 1e-1; % percentage tolerance es = (new-old)/new * 100%
maxit = 60; % Maximum number of iterations
dh = 1e-3; % step size to used in finite differences method to compute the
% Jacobian
Initial_guess = [theta_0; t_0]; % column vector
[x,f,ea,iter]=secantNon_linear(f,Initial_guess,es,maxit,dh);
your_function_Solution=x
function_at_the_found_solution = f
disp('Solution does not converge')
%% TEST THE CODE USING A FUNCTION WITH KNOW SOLUTION
disp(' ')
disp(' ')
disp(' ')
disp('*****************************************************************')
disp('Testing SECANT method with functions with known solution')
disp('fsolve built-in function is used to confirm the solution')
disp('of the test function')
fprintf('Test functions\n')
fprintf(' : f1 = x1.^2+x2.^2-5\n')
fprintf(' : f2 = x2+1-x1.^2\n')
% Here is a test for the code to just confirm the code works
func = @(x1,x2) [x1.^2+x2.^2-5;x2+1-x1.^2];
x0 = [1.2;1.2];
es = 5;
dh = 1e-3;
maxit = 50;
[x,f,ea,iter] = secantNon_linear(func,x0,es,maxit,dh);
secant__TEST_solution = x'
% define the function again in way fsolve can use it: x1 = t(1); x2 = t(2)
func_for_fsolve = @(t) [t(1).^2+t(2).^2-5;t(2)+1-t(1).^2];
fsolve_CONFIRM_solution = fsolve(func_for_fsolve,x0')
%% THE SECANT CODE
function [x,f,ea,iter]=secantNon_linear(fun_xy,Initial_guess,tolerance,maxit,dh)
iter = 0;
x=Initial_guess;
while (1)
f=fun_xy(x(1),x(2));
% Jacobian matrix computed using the finite differences method
dfdx = (fun_xy(x(1)+dh,x(2))-fun_xy(x(1),x(2)))./dh;
dfdy = (fun_xy(x(1),x(2)+dh)-fun_xy(x(1),x(2)))./dh;
J = [dfdx dfdy];
dx=J\f;
x=x-dx;
iter = iter + 1;
ea=100*max(abs(dx./x));
if iter>=maxit||ea<=tolerance, break, end
end
end
