/* From: "COMPUTATIONAL PHYSICS, 2nd Ed" 
   by RH Landau, MJ Paez, and CC Bordeianu 
   Copyright Wiley-VCH, 2007.
   Electronic Materials copyright: R Landau, Oregon State Univ, 2007;
   MJ Paez, Univ Antioquia, 2007; & CC Bordeianu, Univ Bucharest, 2007
   Support by National Science Foundation
*/
//  soliton.c: Solves KdV Equation using finite  difference method 
//  comment: Output data is saved in 3D grid format used by gnuplot 
#include <stdio.h>
#include <math.h>
#define ds 0.4                                            // delta x
#define dt 0.1                                            // delta t
#define max 2000                                       // time steps
#define mu 0.1                              // mu from KdeV equation
#define eps 0.2                              // epsilon from KdeV eq

main() {
  int i, j, k;
  double a1,a2,a3, fac, time, u[131][3];
  FILE *output;                          // save data in soliton.dat
  output= fopen("soliton.dat","w");
  for (i = 0; i<131; i++) u[i][0]= 0.5*(1.-tanh(0.2*ds*i-5.));      
   u[0][1]   = 1.;                                     // end points
   u[0][2]   = 1.;   
   u[130][1] = 0.;  
   u[130][2] = 0.;
   fac = mu*dt/(ds*ds*ds);             
   time= dt;
   for (i = 1; i<130; i++)  {                     // first time step
     a1= eps*dt*(u[i+1][0] + u[i][0] + u[i-1][0]) / (ds*6.0);    
     if ((i>1)&&(i<129))a2=u[i+2][0]+2.0*u[i-1][0]
			                                     -2.0*u[i+1][0]-u[i-2][0];
       else a2= u[i-1][0] - u[i+1][0];
     a3= u[i+1][0]-u[i-1][0];
     u[i][1]= u[i][0] - a1*a3 - fac*a2/3.;       
   }   
   for (j = 1; j<max; j++)  {                // all other time steps
     time+= dt;
     for (i = 1; i<130; i++) {
       a1= eps*dt*(u[i+1][1] + u[i][1] + u[i-1][1]) / (3.0*ds);
       if ((i>1) && (i<129))      a2= u[i+2][1] + 2.0*u[i-1][1] 
				                                - 2.0*u[i+1][1] - u[i-2][1];  
         else a2= u[i-1][1] - u[i+1][1]; 
       a3     = u[i+1][1] - u[i-1][1];
       u[i][2]= u[i][0] - a1*a3 - 2.*fac*a2/3.;     
     }
     for (k = 0; k<131; k++)  {               // move one step ahead
       u[k][0]= u[k][1];
       u[k][1]= u[k][2];
      }
      if ((j%200) == 0) {                   // plot every 200th step
        for (k = 0; k<131; k+= 2)  fprintf(output, "%f\n", u[k][2]);
        fprintf(output, "\n");             // empty line for gnuplot
      }
   } 
   printf("data stored in soliton.dat\n");
   fclose(output);
}