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  1. real :: x0, x, tol, f, dfdx	,df_dx
  2. integer :: max_iter, iter
  3.  
  4. f(x) = x**3-8*x**2+7*x+32  !Equation to solve
  5. dfdx(x) = (f(x + h) - f(x - h)) / (2.0 * h)	!Central Difference Method
  6.  
  7. ! Constants:-
  8. tol = 1.0e-6  ! Tolerance for convergence
  9. max_iter = 100  ! Maximum number of iterations
  10. h=0.001 ! Step-size
  11.  
  12. !Initial Guess x0:-
  13. 1 print*,"Enter the inital Guess:-"
  14. read(*,*)x0
  15.  
  16. ! Function and its derivative at x0:-
  17. fx = f(x0)
  18. df_dx = dfdx(x0)
  19.  
  20. !Checking the validity of the inital guess:-
  21. if(fx > 0.0)then 
  22.    print*,"Initial guess must be such that f(initial guess) should be close to 0."
  23.    goto 1
  24. end if 
  25.  
  26. ! Newton-Raphson iteration:-
  27. iter = 0
  28. do while (abs(fx) >= tol .and. iter < max_iter)
  29.    x = x0 - fx / df_dx  ! Compute next approximation of root
  30.    iter = iter + 1
  31.    x0 = x
  32.    fx = f(x0)
  33.    df_dx = dfdx(x0)
  34. end do
  35.  
  36. ! Output the results:-
  37. if (iter == max_iter) then
  38.    print *,'Newton-Raphson method did not converge within ', max_iter, ' iterations.'
  39. else	    
  40.    print *,'Root found: ',x0
  41.    print *,'Number of iterations: ',iter
  42. end if
  43.  
  44. end
Success #stdin #stdout 0.01s 5312KB
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 Enter the inital Guess:-
 Root found:    3.61507177    
 Number of iterations:            3
https://ideone.com/pr2rmF
language:
Fortran (gfortran 8.3)
created:
12 days ago
visibility:
public

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