//  Euler.java: 常微分方程式のEuler法による解法

import java.io.*;

public class Euler{
 
    public static void main( String argv[] ) throws IOException {

	double min = 0.0;
	double max = 1.0;
    
	double x, y, dx, dy, yreal, yerror, maxerr;

	String s;   

	System.out.println("Input: dx");
	BufferedReader buf = new BufferedReader(new InputStreamReader(System.in));
	s = buf.readLine();
	dx = Double.parseDouble(s);
	System.out.println("dx=" +dx);

	x = min;
	y = 0.0;                                // yの初期条件
	yreal = y;
	yerror = 0.0;
	maxerr=0.0;

	try {
	    PrintWriter pw = new PrintWriter(new FileWriter("euler.dat"));
	    
	    pw.println(x+" "+y+" "+yreal+" "+yerror);

	    while(x <= max)
		{
		    
		    dy = dx*f(x, y);                // yの増分       
		    y += dy;
		    x += dx;    
		    yreal=Math.sin(2.0*Math.PI*x);              // 解析解
		    yerror=y-yreal;                // 誤差=数値解-解析解    

		    if(Math.abs(yerror) > maxerr){
			maxerr=Math.abs(yerror);    // 誤差の絶対値の最大値  
		    }

		    //		    System.out.println("x= " +x + " y= " +y);

		    pw.println(x+" "+y+" "+yreal+" "+yerror);

		}
      
	    pw.close();

	    System.out.println("maxerr= " +maxerr);
	    System.out.println("data stored in euler.dat");
      
	} catch (Exception e) {
	    System.err.println("File output error: " + e);
	}

        
    }

    public static double f(double x, double y)
    {
	return(2.0*Math.PI*Math.cos(2.0*Math.PI*x));               /* dy/dx */
    }
    
}