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By: a guest on Mar 16th, 2012  |  syntax: None  |  size: 1.89 KB  |  views: 49  |  expires: Never
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  1. public class Runge2{
  2.  
  3.     public static double f(double x, double y){
  4.         double f = Math.pow(x,5) * Math.pow(Math.E,Math.pow(x,3));
  5.         return f;
  6.     }
  7.  
  8.     /* This is the Runge Function given in class */
  9.  
  10.     public static double rk(double x, double y, double step){
  11.         double h = step;
  12.         double k1 = h * f(x, y);
  13.         double k2 = h * f(x + h/2, y + k1/2);
  14.         double k3 = h * f(x + h/2, y + k2/2);
  15.         double k4 = h * f(x + h, y + k3);
  16.  
  17.         return y += k1/6 + k2/3+ k3/3 + k4/6;
  18.     }
  19.  
  20.     public static void main(String[] args){
  21.  
  22.  
  23.  
  24.         try{
  25.  
  26.         double stepSize = Double.parseDouble(args[0]);
  27.  
  28.  
  29.         /* this sets the range of the integral */
  30.  
  31.         double initial = 0;
  32.         double end = 1;
  33.  
  34.         /* steps is total steps and finalY is the value of the integral */
  35.  
  36.         double steps = (end - initial) / stepSize;
  37.         double i = 0;
  38.         double finalY = 0;
  39.  
  40.         if (stepSize <= 0)
  41.             throw new Exception("Error: Stepsize is negative or 0. \n");
  42.  
  43.         for (i = 0; i < steps ; i++){
  44.             finalY += rk(initial + i * stepSize,
  45.                          0, stepSize);
  46.         }
  47.  
  48.         System.out.printf("The Runge Kutta method gives the value \n" );
  49.         System.out.printf("%1.4f as the integral of x^5 * e^x^3  \n",
  50.                           finalY);
  51.         System.out.printf("on the interval of %1.4f to %1.4f  \n",
  52.                           initial, end );
  53.         System.out.printf("using %1.0f steps and a step size of %1.6f \n",
  54.                           steps,stepSize);
  55.  
  56.         if (stepSize > 1.0)
  57.             throw new Exception("Warning: Stepsize is large. Values may be off.\n");
  58.         }
  59.  
  60.         catch(Exception e){
  61.             System.out.printf(e.getMessage());
  62.             System.out.printf("\nYou need to input a float point value \n");
  63.             System.out.printf("For the value of the step size. To get a \n");
  64.             System.out.printf("reasonable answer, this step size should \n");
  65.             System.out.printf("be fairly small, non-negative and entered \n");
  66.             System.out.printf("as a command line argument, thank you. \n");
  67.  
  68.         }
  69.  
  70.  
  71.     }
  72. }