数值积分_自适应辛普森法

#include<stdio.h>

#include<math.h>

double F(double x){return log10(x);}

//三点辛普森公式

double simpson(double width,double fa,double fb,double fc)

{

return (fb+fa+4*fc)*width/6;

}

//自适应simpson公式递归过程

double asr(double a,double b,double eps,double A)

{

double c=(a+b)/2;

double fa,fb,fc,L,R;

fa=F(a);fb=F(b);fc=F(c);

L=simpson(c-a,fa,fc,F((c+a)/2));

R=simpson(b-c,fc,fb,F((b+c)/2));

if(fabs(L+R-A)<=15*eps) return L+R+(L+R-A)/15;

return asr(a,c,eps/2,L)+asr(c,b,eps/2,R);

}

//自适应simpson公式主过程

double asr(double a,double b,double eps)

{

return asr(a,b,eps,simpson(b-a,F(a),F(b),F((b+a)/2)));

}

int main()

{

printf("%lf\n",asr(1,5,0.00000001));

return 0;

}