///////////////////////////////////////////////////////////////////////////////////////////////////////////
//                                                                                                       //
// ----------------------------  Ebrahim Foulaadvand, 08 may 2012  ------------------------------------  //
//                                                                                                       //
// -- The programme "NuclearDecay" evaluates the time dependence of number of undecayed                  //
//                                                                                                       //
//   radioactive nuclei. Comparison is done with analytical solution.                                    //                 //
//                                                                                                       //
//                                                                                                       //
///////////////////////////////////////////////////////////////////////////////////////////////////////////

#include <iostream>
#include <fstream>
#include <conio>
#include <math.h>
#include <numeric>
#include <values>
#include <vector>
#include <list>
#include <algorithm>
#include <numeric>
#include<iomanip.h>

using namespace std;


double  tau=0.01, N0=1000., r=0.2; // tau=time step, N0=intial number of radioactive nuclei, r=decay rate.

int T=2000,n; // T=number of time steps.

main()
{

ofstream  fileN ("N-t r=0.2.plt"); // output file for time dependence of nuclei number.
ofstream  fileNanal ("Nanal-t r=0.2.plt"); //output file for the analytical time dependence of nuclei number.


vector<double> N(T+1,0),Nanal(T+1,0); // Array N stores the number of undecayed nuclei at time step n.



// ----------------------- initial conditions --------------------

N[0]=N0;

for(int n=0;n<T; n++){

N[n+1]=N[n]*(1-r*tau);

fileN<<n*tau<<" "<<N[n]<<endl;

fileNanal<<n*tau<<" "<<N0*exp(-r*n*tau)<<endl;

}

cout<<"end."<<endl;getch();

return 0;

}