自适应辛普森积分

Module Simpson_mod
  Implicit none
  Real(kind=8) :: a = 0.d0, b = 1.d0  !// 积分区间
  Real(kind=8) :: pi = acos(-1.d0), eps = 1.d-8, s0
  Real(kind=8) :: calPi = 0.d0  !// 数值积分解 
Contains
  Real(kind=8) function func ( x )
    Implicit none
    Real(kind=8) :: x
    
    func = 4.d0 / ( 1.d0 + x * x )  !// 此函数的积分值为pi
  End function func
  
  Recursive Real(kind=8) function simpson ( atmp, btmp, eps, s ) result( calPi )
    Implicit none
    Real(kind=8), intent(in) :: atmp, btmp, eps, s
    Real(kind=8) :: h, s1, s2
    
    h = ( btmp - atmp ) / 2.d0
    s1 = h / 6.d0 * ( func(atmp) + func(atmp+h/2.d0) + 4.d0*func(atmp+h/2.d0) )
    s2 = h / 6.d0 * ( func(atmp+h) + func(btmp) + 4.d0*func(atmp+3.d0/2.d0*h) )
    if ( abs( s - s1 - s2 ) < 15.d0*eps ) then
      calPi = s1 + s2
    else
      calPi = simpson( atmp, (atmp+btmp)/2.d0, eps/2.d0, s1 ) + simpson( (atmp+btmp)/2.d0, btmp, eps/2.d0, s2 )
    end if
  End function simpson
End module Simpson_mod
  
Program AdaptiveSimpson
  use Simpson_mod
  Implicit none
  !// 第一次计算simpson积分
  s0 = ( b-a ) / 6.d0 *( func(a) + func(b) + 4.d0*func(1.d0/2.d0*(a+b)) )
  calPi = simpson( a, b, eps, s0 )
  Write( *, '(1x,a,2x,g0)') "the integral is", calPi
  Write( *, '(1x,a,2x,g0)') "the absolute error is", abs(pi-calPi)
End program AdaptiveSimpson 

 

来源：CSDN

作者：chd_lkl

链接：https://blog.csdn.net/chd_lkl/article/details/103598109