/*************************    Program 3.1    ****************************/
/*                                                                      */
/************************************************************************/
/* Please Note:                                                         */
/*                                                                      */
/* (1) This computer program is written by Tao Pang in conjunction with */
/*     his book, "An Introduction to Computational Physics," published  */
/*     by Cambridge University Press in 1997.                           */
/*                                                                      */
/* (2) No warranties, express or implied, are made for this program.    */
/*                                                                      */
/************************************************************************/

#include <stdio.h>
#include <math.h>
#define NMAX 101

main()
/* Simplest predictor-corector algorithm applied to a
   particle in one dimension under an elastic force.
   Copyright (c) Tao Pang 1997. */
{
int i,n,m;
double dt,pi;
double t[NMAX],x[NMAX],v[NMAX];

n = NMAX;
m = 5;
pi = 4*atan(1);
dt = 2*pi/100;
x[0] = 0;  t[0] = 0;  v[0] = 1;
for (i = 0; i < n-1; ++i)
  {
  t[i+1] = (i+1)*dt;

/* Predictor for position and velocity */

  x[i+1] = x[i]+v[i]*dt;
  v[i+1] = v[i]-x[i]*dt;

/* Corrector for position and velocity */

  x[i+1] = x[i]+(v[i]+v[i+1])*dt/2;
  v[i+1] = v[i]-(x[i]+x[i+1])*dt/2;
  if (i == 0 || (i+1)%m == 0)
    printf("%16.8lf %16.8lf %16.8lf\n", t[i],x[i],v[i]);
  }
}