Runge-Kutta

#include <stdio.h>
#define _USE_MATH_DEFINES
#include <math.h>
#define G 9.80665
#define N 1000
double f(double t) {
  return 780. * cos(M_PI_4);
}
double g(double t) {
  return 780. * sin(M_PI_4) - G * t;
}
void runge(int n, double t_begin, double t_end, double x0, double y0, double *x,
    double *y) {
  int i;
  double t, h, h2, f1, f2, f3, f4, g1, g2, g3, g4;
  t = t_begin;
  h = (t_end - t_begin) / n;
  h2 = h / 2;
  *x = x0;
  *y = y0;
  for (i = 1; i <= n; i++) {
    f1 = h * f(t);
    f2 = h * f(t + h2);
    f3 = h * f(t + h2);
    f4 = h * f(t + h);
    g1 = h * g(t);
    g2 = h * g(t + h2);
    g3 = h * g(t + h2);
    g4 = h * g(t + h);
    t += h;
    *x += (f1 + 2 * f2 + 2 * f3 + f4) / 6;
    *y += (g1 + 2 * g2 + 2 * g3 + g4) / 6;
  }
}
int main(void) {
  double t_begin = 0., t_end = 1000., x0 = 0., y0 = 0., x, y;
  runge(N, t_begin, t_end, x0, y0, &x, &y);
  printf("% -lf % -lf\n", x, y);
  printf("% -lf % -lf\n", 780. * cos(M_PI_4) * 1000.,
    780. * sin(M_PI_4) * 1000. - G / 2. * 1000. * 1000.);
  return 0;
}