/*
************************************************************************
*  ルンゲ・クッタ法による1次元運動方程式の解法                         *
*  投げ上げ                                                            *
*   t：時間、x ：位置 、v：速度                                        *
*   dt：時間の刻み幅                                                   *
*   t0、x0、v0：初期値                                                 *
*                                                                      * 
************************************************************************
*/
       
#include <stdio.h>
#include <math.h>

 
main()
{
   double f(double t, double x, double v, int i);
   
   double t, x, v, x0, v0, dt, h, xreal, xerror;
   int j;
   double t10, t11, t20, t21, t30, t31,       /* Runge-Kutta法のための */
     k10, k11, k20, k21, k30, k31 ,k40, k41;  /* 一時変数     */
   
   FILE *output;
   output = fopen("fall.dat","w");            /* fall.datにデータをセーブ */

   printf("Input: v0\n");
   scanf("%lf", &v0);
   printf("v0=%g\n", v0);
   printf("Input: dt\n");
   scanf("%lf", &dt);
   printf("dt=%g\n", dt);
   
   t = 0;
   x0 = 0.0;
   x = x0;                                /* 初期位置  */
   v = v0;                                 /* 初期速度  */
   
   fprintf(output, "%f\t%f\n", t, x);

   while(x >= 0)
   {

      k10 = dt*f(t, x, v, 0);
      t10 = x+0.5*k10;
      k11 = dt*f(t, x, v, 1);
      t11 = v+0.5*k11;
      
      k20 = dt*f(t+h, t10, t11, 0);
      t20 = x+0.5*k20;
      k21 = dt*f(t+h, t10, t11, 1);
      t21 = v+0.5*k21;
      
      k30 = dt*f(t+h, t20, t21, 0);
      t30 = x+    k30;
      k31 = dt*f(t+h, t20, t21, 1);
      t31 = v+    k31;
      
      k40 = dt*f(t + dt, t30, t31, 0);
      k41 = dt*f(t + dt, t30, t31, 1);
      
      x += (k10+2*k20+2*k30+k40)/6.0;
      v += (k11+2*k21+2*k31+k41)/6.0;

      t += dt;    
      xreal=v0*t-0.5*9.8*t*t;                 /* 解析解 */
      xerror=x-xreal;                      /* 誤差=数値解-解析解 */ 
      fprintf(output, "%f\t%f\t%f\t%e\n", t, x, xreal, xerror);
   }
   printf("data stored in fall.dat\n");
   fclose(output);
}
/*--------------------------------------------------------------------*/

/* 微分方程式の右辺 */
double  f(double t, double x, double v, int i)
{
   if (i == 0) return(v);                  /* dx/dt*/
   if (i == 1) return(-9.8);               /* dv/dt*/
}