龙格-库塔算法.cpp

高斯赛德尔迭代法

#include<iostream.h>

void main()
{
	void Runge_Kutta(float (*f)(float,float),float a,float b,float y0,int N);
	float f(float,float);
	float a=0,b=5,y0=2;
	Runge_Kutta(f,a,b,y0,20);
}
void 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;
	float h=(b-a)/N;
	int i;
	cout<<"x[0]="<<x<<'\t'<<"y[0]="<<y<<endl;
	for(i=1;i<=N;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;
		cout<<"x["<<i<<"]="<<x<<"    y["<<i<<"]="<<y<<endl;
	}
}
float f(float x,float y)
{
	return -x*y*y;
}