% Demonstration of Root Finding using False Position
%

function y = fcn(x)
y = 9.8 * 68.1 * (1-exp(-10*x/68.1))/x - 40;
end 



xl = 1;   % 'Enter lower bound of root bracket;
xu = 4;   % 'Enter upper bound of root bracket;
maxerror = 0.01;  % 'Enter maximum error ;
maxit = 100;  % 'Enter maximum number of iterations;

count = 0;          % iteration counter
rel_error = 1;      % to force entry into while loop
xr = xu;            % require starting value in loop below

write("xl  ","xu  ","xr  ","error  ");

% main loop until change between iterations small enough

while (rel_error > maxerror) & (count < maxit) 
  count = count + 1;
  xrold = xr;

  xr = xu - fcn(xu)*(xu-xl)/(fcn(xu)-fcn(xl));
  

  if xr ~= 0
    rel_error = abs((xr - xrold)/xr) * 100;
  end
  write(xl,"  ",xu,"  ",xr,"  ",rel_error);

  test = fcn(xl) * fcn(xr);  % form test product

  if test == 0
    rel_error = 0;  % root is at xr
  else if test < 0
    xu = xr;        % root is below xr
  else
    xl = xr;        % root is above xr
  end
end
end