Question

解题的过程和复化SIMPSON公式

Answer 1

#include "stdio.h"

#include "math.h"

double P4(double x)

{

x09return (1.0 + x + x*x/2.0 + pow(x,3)/6.0 + pow(x,4)/24.0);

}

double G(double x)

{

x09if ( 0

x09{

x09x09return ( (exp(x)-P4(x))/sqrt(x) );

x09}else

x09{

x09x09return 0;

x09}

}

double H()

{

x09int i;

x09double f1=0,f2=0;

x09double m[]={1,1,1.0/2,1.0/6,1.0/24};

x09double n[]={-1.0/2,1.0/2,3.0/2,5.0/2,7.0/2 };

x09for(i=0;i<5;i++)

x09{

x09x09m[i]=m[i]/(n[i]+1);

x09x09n[i]=n[i]+1;

x09}

x09for(i=0;i<5;i++)

x09{

x09x09f1+=m[i]*pow(0,n[i]);

x09x09f2+=m[i]*pow(1,n[i]);

x09}

x09

x09return (f2-f1);

}

double Simpson(double a, double b, double h, double (*f)(double))

{

x09double xk;

x09double sk = 0,sk2 = 0;

x09double Sn = 0;

x09double n;

x09int i;

x09n = (b-a)/h;

x09sk2 = f(a+h/2.0);

x09for (i=1; i

x09{

x09x09xk = a+h*i;

x09x09sk += f(xk);

x09x09sk2 += f(xk+h/2.0);

x09}

x09Sn = f(a) + 2.0*sk + f(b) + 4.0*sk2;

x09Sn = Sn*h/6.0;

x09return Sn;

}

double Int()

{

x09return (H()+Simpson(0, 1, 0.25, G));

}

void main()

{

x09printf("H = %lfn", H());

x09printf("Int(Gx) = %lfn", Simpson(0, 1, 0.25, G));

x09printf("answer = %lfn", Int());

}