////////////////////////////////////////////////////////////////////////////////////////////////////////////
//                                                                                                        //
// ------------------------ Ebrahim Foulaadvand & somayyeh Belbaasi, 22 Oct. 2008 ----------------------- //
//                                                                                                        //
// --- The programme "CoffeeCool" evaluates the temporal evolution of the temperature of a coffee cup     //
//  by the Euler algorithm.                                                                                //
//                                                                                                        //
//                                                                                                        //
//                                                                                                        //
////////////////////////////////////////////////////////////////////////////////////////////////////////////


#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, Ts=0., T0=100., r=1;

//tau=time step, Ts=surrounding temperature, T0=initial temperature of coffee cup, r=cooling rate                                                                                                                //

int N=2000,t; // N=number of time steps

main()

{

ofstream  fileT ("T-t.plt"); // output file for the time dpendence of temperature.

vector<double> T(N+1,0); // Array T stores the coffee temperature at time step t.


T[0]=T0; // -------- initial condition -------------


//---------------------- Euler-Cromer Method---------------------

for(int t=0;t<N; t++){

T[t+1]=T[t]-r*tau*(T[t]-Ts);

fileT<<t*tau<<" "<<T[t]<<endl;

}

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

return 0;

}