Método de Euler III (osc. harmônico)

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

#define x0 2

#define v0 1

#define t0 0
#define tf 100

#define w02 3

#define dt 1e-2
#define N ((tf-t0)/dt)

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

int main(void)
{
    double x = x0, xn,
           t = t0, tn,
           v = v0, vn;
    int i;

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

    for (i = 0; i < N; ++i)
    {
        xn  = x + v*dt;
        vn = v + dvdt(x,v,t)*dt;
        tn = t + dt;

        fprintf(h, "%d %f %f\n", i, t, x);

        x = xn;
        v = vn;
        t = tn;
    }

    fclose(h);
    return 0;
}