Fortran 95 source code to solve nonlinear-equation with bisection method.

nonlinear_equation_bisection.f95

!****************************************************
! 非線形方程式の解法（二分法）
! * 方程式： y = x + cos(2 * x) - sin(4 * x)
!
! date          name            version
! 2018.10.11    mk-mode.com     1.00 新規作成
!
! Copyright(C) 2018 mk-mode.com All Rights Reserved.
!****************************************************
!
program nonlinear_equation_bisection
  implicit none
  ! SP: 単精度(4), DP: 倍精度(8)
  integer,      parameter :: SP = kind(1.0)
  integer(SP),  parameter :: DP = selected_real_kind(2 * precision(1.0_SP))
  integer(SP),  parameter :: NMAX = 50
  real(DP),     parameter :: EPS = 1.0e-6
  logical     :: stat
  integer(SP) :: n
  real(DP)    :: x, y, x_0, x_1, sgn

  write (*, "(a)", advance="no") "x_0, x_1 : "
  read (*,*) x_0, x_1

  ! x_0 > x_1 であれば、交換
  if (x_0 > x_1) then
     x   = x_0
     x_0 = x_1
     x_1 = x
  end if

  ! f(x_0) と f(x_1) の符号が逆なら、終了
  if (f(x_0) * f(x_1) >= 0.0) then
     write (*,*) "f(x_0) * f(x_1) >= 0.0"
     stop
  end if

  sgn = sign(1.0_8, f(x_1) - f(x_0))
  stat = .false.
  do n = 1, NMAX
     x = (x_0 + x_1) * 0.5_8
     y = f(x)

     ! 収束判定
     if (abs(x_1 - x_0) < EPS) then
        stat = .true.
        write(*, '("収束 [", i4, "]")') n
        exit
     else
        write(*, '("誤差 [", i4, "] = ", e20.8)') n, abs(y)
     end if

     ! 次の値を推定
     if (y * sgn < 0.0) then
        x_0 = x
     else
        x_1 = x
     end if
  end do

  ! 結果出力
  if (.not. stat) then
     write (*, *) "近似不可！"
  end if
  write (*, '("近似値 = ", e20.8)') x
  write (*, '("誤差   = ", e20.8)') abs(y)

  stop
contains
  ! 方程式
  ! * f = x + cos(2 * x) - sin(4 * x)
  !
  ! :param  real(8) x
  ! :return real(8) f
  real(DP) function f(x)
    implicit none
    real(DP), intent(in) :: x

    f = x + cos(2 * x) - sin(4 * x)
  end function f
end program nonlinear_equation_bisection