#include <stdio.h>
#include <math.h>

#define x0 2

#define v0 1

#define t0 0
#define tf 2.5

#define dt0 0.01
#define dtf 1e-6
#define ddt -1e-4

#define w02 3
#define Ndt ((dtf-dt0)/ddt)

double dvdt(double x, double v, double t)
{
	return -w02*x;
}

double E(double x, double v)
{
	return v*v/w02 + x*x;
}

int main(void)
{
	double x, xn, 
	       t, tn, 
	       v, vn,
	       dt;

	FILE *h = fopen("./eulerdt.dat","w+");

	for(int k = 0; k < Ndt; k++)
	{
		dt = dt0 + k * ddt;

		x = x0; t = t0; v = v0;

		double E0 = E(x,v);

		for (int i = 0; i < ((tf-t0)/dt); ++i)
		{
			vn = v + dvdt(x,v,t)*dt;
			xn = x + vn*dt;
			tn = t + dt;
	
			x = xn;
			v = vn;
			t = tn;
		}
		fprintf(h, "%f %f\n", dt, E(x,v)/E0-1);
	}

	fclose(h);
	return 0;
}