// Euler-Verfahren fuer den harmonischen Oszillator
// bash: export CLASSPATH=.:~/lib/java

import HUMath.Algebra.*;

class Euler {

public static void main(String[] args){
  
  double t=0, x=1, y=0, h=0.05;

  while(t<20){
    double v=y;
    B.wl("\t"+t+"\t"+x+"\t"+y);
    y-=h*x;
    x+=h*v;
    t+=h;
    }
  }

}


/*
Approximation hat Werte auf cos(a*x)*exp(b*x) mit

bash:
java Euler > e0050.dat

gnuplot:
fit cos(a*x)*exp(b*x) './e0050.dat' via a,b
pl './e0050.dat' u 1:2, cos(a*x)*exp(b*x)

h = 0.5
a = 0.927295         +/- 9.902e-18    (1.068e-15%)
b = 0.223144         +/- 1.229e-17    (5.507e-15%)

h = 0.2
a = 0.986978         +/- 4.363e-17    (4.42e-15%)
b = 0.0980518        +/- 3.805e-17    (3.881e-14%)

h = 0.1
a = 0.996687         +/- 6.792e-17    (6.814e-15%)
b = 0.0497517        +/- 6.172e-17    (1.241e-13%)

h = 0.05
a = 0.999168         +/- 1.281e-16    (1.283e-14%)
b = 0.0249688        +/- 1.194e-16    (4.782e-13%)

*/