ch7_3_1.java

Java环境下实现的数值分析程序

class ch7_3_1{
	static double f(double x,double y){
		return Math.pow(y,2);
	}
	static double[] Runge_Kutta(double x0,double y0,double xn,int n){
		double K1=0.0;
		double K2=0.0;
		double K3=0.0;
		double K4=0.0;
		double x=x0;
		double y=y0;
		double []yy=new double[3];
		double h=(xn-x0)/n;
		System.out.println("x[0]="+x+" "+"y[0]="+y);
		for(int i=1;i<=3;i++){
			K1=f(x,y);
			K2=f(x+((xn-x0)/n)/2.0,y+((xn-x0)/n)*K1/2.0);
			K3=f(x+((xn-x0)/n)/2.0,y+((xn-x0)/n)*K2/2.0);
			K4=f(x+((xn-x0)/n),y+((xn-x0)/n)*K3);
			y=y+h*(K1+2*K2+2*K3+K4)/6.0;
			x=x0+i*h;
			yy[i-1]=y;
			System.out.println("x["+i+"]="+x+" "+"y["+i+"]="+yy[i-1]);
		}
		return yy;
	}
	static void Adams(double x0,double y0,double xn,int n){
		double x=0.0;
		double y1=0.0;
		double y2=0.0;
		double y=0.0;
		double yp=0.0;
		double yc=0.0;
		double []yy=Runge_Kutta(x0,y0,xn,n);
		y1=yy[0];
		y2=yy[1];
		y=yy[2];
		double h=(xn-x0)/n;
		for(int i=4;i<=n;i++){
			x=x0+i*h;
			yp=y+(h/24.0)*(55.0*f(x,y)-59.0*f(x-h,y2)+37.0*f(x-2.0*h,y1)-9.0*f(x-3.0*h,y0));
			yc=y+(h/24.0)*(9.0*f(x+h,yp)+19.0*f(x,y)-5.0*f(x-h,y2)+f(x-2.0*h,y1));
			System.out.println("x["+i+"]="+x+" "+"y["+i+"]="+yc);
			y0=y1;
			y1=y2;
			y2=y;
			y=yc;
		}
	}		
	public static void main(String []args){
		double xn=1.0;
		double x0=0.0;
		double y0=1.0;
		int n=10;
		Adams(x0,y0,xn,n);
	}
}