/* 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
*/
//  Shock.c Solve Burger's shock equation using Lax-Wendroff scheme 

#include<stdio.h>
#include<math.h>
#define m 100  //number of grid points
  
main() {
	
  FILE *output1,*output2;
  output1 = fopen("numerical.dat","w"); // solution in  numerical.dat
  output2 = fopen("initial.dat","w");            // initial condition
  double u[m],  u0[m],  epsilon= 1.0,  beta = 0.1;  //CFL number beta
  double x, dx, dt, T_final;
  int i, j, n;
	
  dx = 2.0/m;                                           // space step
  dt = beta*dx/epsilon;                                  // time step
  T_final = 0.15;
  n = (int)(T_final/dt);
	
  for (i = 0;i<m-1;i++)  {                             //initial data
    x= i*dx;
    u0[i]= 3.0*sin(3.2*x);
    fprintf(output2,"%f\t%f\n",0.01*i,u0[i]);    // save initial data
  }
	                                             // Lax-Wendroff scheme
  for (j = 1;j<n;j++) {                         
    for (i = 0;i<m-3;i++){
			
      u[i+1]= u0[i+1]- (pow(u0[i+2],2)-pow(u0[i],2))*(0.25*beta)+
        (((u0[i+2]+u0[i+1])/2.0)*(pow(u0[i+2],2)-pow(u0[i+1],2))- 
        ((u0[i+1]+u0[i])/2.)*(pow(u0[i+1],2)
				                            -pow(u0[i],2)))*0.25*beta*beta;
								
      u[0] = 0.0; u[m-1] = 0.0;
      if ((j%5 == 0)&&(i%4 == 0))  fprintf(output1,"%f\n ",u[i]);
      u0[i]= u[i];                                // shift new to old
    }
    if (j%5 == 0)fprintf(output1,"\n");
  }
  printf("Numerical solution data saved in numerical.dat");
}                                                             // main