% Matlab script to illustrate the secant method
% to solve a nonlinear equation
% this particular script finds the square root of a number M
% (input by the user)
% note that the function we are trying to zero is f(x) = x^2 - M.
% this function is hard-coded in the script.
g=9.8065;
k=0.00341;
% f(x)=log(cosh(t*srt(g*k)))/k;
format long
% get user input
M = input(‘Please enter the number whose square root you want: ‘)
t0 = input(‘Please enter the first of two starting guesses: ‘)
t1 = input(‘Please enter the second of two starting guesses: ‘)
% iteration counter
k = 1
% compute first secant iterate to enter loop
s = (((log(cosh(t1*sqrt(g*k)))/k)-M)-((log(cosh(t0*sqrt(g*k)))/k)-M) )/(t1-t0);
% s = ( (x1^2-M) - (x0^2-M) ) / (x1 - x0);
t = t1 - (((log(cosh(t1*sqrt(g*k)))/k)-M))/s
% x = x1 - (x1^2-M)/s
disp(‘Hit return to continue‘)
pause
while abs(t-t1) > eps*abs(t),
% reset guesses
t0 = t1;
t1 = t;
% increment iteration counter
k = k + 1
% compute and display secant iterate
s = (((log(cosh(t1*sqrt(g*k)))/k)-M)-((log(cosh(t0*sqrt(g*k)))/k)-M) )/(t1-t0);
% s = ( (x1^2-M) - (x0^2-M) ) / (x1 - x0);
% x = x1 - (x1^2-M)/s
t = t1 - (((log(cosh(t1*sqrt(g*k)))/k)-M))/s
disp(‘Hit return to continue‘)
pause
end