difequation.cpp

C++实现的数值分析源程序

//梁霄 11/24/2005
#include"DifEquation.h"
//欧拉方法和改进欧拉方法
double Euler::f(double x,double y)
{
	return y-2*x/y;
}
void Euler::CommonEuler(double x0,double y0,double step)
{
	double yn=0.0;

	cout<<"--------Euler Method--------"<<endl;
	for(int i=0;i<=10;i++)
	{
		if(i==0)
			yn=y0;
		else
		{
			yn+=step*f(x0,yn);
			x0+=step;
		}
		cout<<"x:"<<x0<<'\t'<<"y:"<<yn<<endl;
	}
}
void Euler::ImprEuler(double x0,double y0,double step)
{
	double yp=0.0,yc=0.0,yn=0.0;

	cout<<"--------Improved Euler Method--------"<<endl;
	for(int i=0;i<=10;i++)
	{
		if(i==0)
			yn=y0;
		else
		{
			yp=yn+step*f(x0,yn);
			yc=yn+step*f(x0+step,yp);
			yn=0.5*(yp+yc);
			x0+=step;
		}
		cout<<"x:"<<x0<<'\t'<<"y:"<<yn<<endl;
	}
}
//四阶龙格库塔方法
double RongeKutta::f(double x,double y)
{
	return y-2*x/y;
}
void RongeKutta::RongeKutta4(double x0,double y0,double step)
{
	double yn=0.0,K1=0.0,K2=0.0,K3=0.0,K4=0.0;

	cout<<"--------4-Order Ronge-Kutta Method--------"<<endl;
	for(int i=0;i<=10;i++)
	{
		if(i==0)
			yn=y0;
		else
		{
			K1=f(x0,yn);
			K2=f(x0+step/2,yn+step*K1/2);
			K3=f(x0+step/2,yn+step*K2/2);
			K4=f(x0+step,yn+step*K3);
			yn+=step*(K1+2*K2+2*K3+K4)/6;
			x0+=step;
		}
		cout<<"x:"<<x0<<'\t'<<"y:"<<yn<<endl;
	}
}