***REGULA FALSI METHOD************************************************
*      THIS PROGRAM FINDS THE ROOT OF AN ALGEBRAIC/TRANSCENDENTAl    *
*                  EQUATION BY REGULA FALSI METHOD                   *
**********************************************************************
*
      program REGULAFALSI
      implicit doubleprecision(a-h,o-z)
c
c     Defining the Function 'F(x)=0' to be solved
      F(x) = x**2 - 10*x + 3d0
*
      print*, 'Enter lower limit (guessed) of the interval, xl:'
      read(*,*) xl
      print*, 'Enter upper limit (guessed) of the interval, xu:'
      read(*,*) xu
      prod = F(xl) * F(xu)
*
      if (prod > 0d0) then
         write(6,*)'The root does not lie within the bracketed interval.'
         stop
      elseif (prod == 0d0) then
         if (F(xl) == 0d0) then
            print*, 'The exact root of the equation is:', xl
         else
            print*, 'The exact root of the equation is:', xu
         endif
         print*, 'No iterations performed'
         stop
      else
         i = 1
         error = 1d9
         tolerance = 1d-5
         max_iter  = 3
         xr = xu - F(xu)*(xl - xu)/(F(xl) - F(xu))
10       if ((error > tolerance).and.(i < max_iter)) then 
            prod = F(xl) * F(xr)
            if (prod < 0d0) then
               xu = xr
            elseif (prod > 0d0) then
               xl = xr
            elseif (prod == 0d0) then
               print*, 'The root of the equation is:', xr
               print*, 'Number of iterations performed:', i
               stop
            endif
            xr_old = xr
            xr = xu - F(xu)*(xl - xu)/(F(xl) - F(xu))
            error = dabs((xr - xr_old)/xr)*100
            i = i + 1
            go to 10
         endif
      endif
*
      if (error <= tolerance) then
         print*, 'The root of the equation is:', xr
         print*, 'Number of iterations performed:', i
      else
         print*, 'The root is not reached within the error limit after t
     $he prescribed number of iteration,', i
      endif     
*
      stop
      end