四阶阿当姆斯预测-校正公式-cpp.txt

四阶阿当姆斯预测-校正公式-cpp.txt

#include<iostream.h> 

float f(float x,float y) 
{ 
return -x*y*y; 
} 
float *Runge_Kutta(float (*f)(float x,float y),float a,float b,float y0,int N) 
{ 
float x=a,y=y0,K1,K2,K3,K4,*yy; 
float h=(b-a)/N; 
int i; 
yy=new float[(sizeof(float)*3)]; 
for(i=1;i<=3;i++) 
{ 
K1=f(x,y); 
K2=f(x+h/2,y+h*K1/2); 
K3=f(x+h/2,y+h*K2/2); 
K4=f(x+h,y+h*K3); 
y=y+h*(K1+2*K2+2*K3+K4)/6; 
x=a+i*h; 
*(yy+i-1)=y; 
} 
return yy; 
} 
void Adams(float a,float b,int N,float (*f)(float x,float y),float y0) 
{ 
int i; 
float y1,y2,y,yp,yc,*yy,h,x; 
cout<<"x[0]="<<a<<'\t'<<" y[0]="<<y0<<endl; 
yy=Runge_Kutta(f,a,b,y0,N); 
y1=yy[0]; 
y2=yy[1]; 
y=yy[2]; 
h=(b-a)/N; 
for(i=1;i<=3;i++) 
cout<<"x["<<i<<"]="<<a+i*h<<" y["<<i<<"]="<<*(yy+i-1)<<endl; 
for(i=3;i<N;i++) 
{ 
x=a+i*h; 
yp=y+h*(55*f(x,y)-59*f(x-h,y2)+37*f(x-2*h,y1)-9*f(x-3*h,y0))/24.0; 
yc=y+h*(9*f(x+h,yp)+19*f(x,y)-5*f(x-h,y2)+f(x-2*h,y1))/24.0; 
cout<<"x["<<i+1<<"]="<<x+h<<" y["<<i+1<<"]="<<yc<<endl; 
y0=y1; 
y1=y2; 
y2=y; 
y=yc; 
} 
} 
void main() 
{ 
float a=0,b=5.0,y0=2.0; 
int N=20; 
Adams(a,b,N,f,y0); 
}