adams73.java

数值分析之计算方法与实验7：常微分方程数值解法 by java

//阿当姆斯方法 
import java.io.*;
class Adams73{
  static double f(double x,double y){
     return y*y;
  }
  static double [] RK(double a,double b,double y0,int n){
    double x=a,y=y0,k1,k2,k3,k4;
    double yy[]=new double[4];
    double h=(b-a)/n;
    int i;
    yy[0]=y0;
    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+k3*h);
      y=y+h*(k1+2*k2+2*k3+k4)/6;
      x=a+i*h;
      yy[i]=y;
    }
    return yy;
  }
  static void admas(double a,double b,double y0,int n)throws IOException{
  	PrintWriter out = new PrintWriter(new FileWriter("result.txt"));
    int i;
    double y1,y2,y,yp,yc,h,x;
    h=(b-a)/n;
    double yy[]=new double[n];
    out.print("x[0]="+a+"  y[0]="+y0+"\n");
    yy=RK(a,b,y0,n);
    y1=yy[0];
    y2=yy[1];
    y=yy[2];
    for(i=1;i<=3;i++)out.print("x["+i+"[="+(a+i*h)+"  y["+i+"]="+yy[i]+"\n");
    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;
      out.print("x["+(i+1)+"]="+(x+h)+"  y["+(i+1)+"]="+yc+"\n");
      y0=y1;
      y1=y2;
      y2=y;
      y=yc;
    }
    out.close(); 
  }
  public static void main(String[]args)throws IOException{
     double a=0.0,b=1.0,y0=1.0;
     int n=20;
     admas(a,b,y0,n); 
  }
}