四阶阿当姆斯预测-校正公式.cpp

高斯赛德尔迭代法

#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);
}