#include <iostream>
#include <fstream>
#include <cmath>
#include <valarray>

using namespace std;

int main() {
    double T, dt;

    cout << "Stabilita: reseni diferencialni rovnice metodou 1. radu" << endl;

    cout << "Zadejte maximalni cas T: "; cin >> T;
    cout << "Zadejte krok dt:         "; cin >> dt;

    int N = T / dt;
    cout << "Pocet kroku:             " << N << endl;

    valarray<double> v(N);
    valarray<double> v_exact(N);

    v_exact[0] = exp(0);
    v_exact[1] = exp(-dt);
    
    v[0] = 1;           // Pocatecni podminka v(0) = v0;
    v[1] = v_exact[1];  // 3-bodove schema potrebuje 2 pocatecni hodnoty  
    
    // diferencni schema v(t+dt) - v(t-dt) / 2dt = -v(t)
    for(int i = 2 ; i < N ; ++i){
        v[i]        = v[i-2] - 2*dt*v[i-1];
        v_exact[i]  = exp(-i*dt);
    }

    ofstream file;
    file.open("pad_meteoritu2.txt");
    for(int i = 0; i < N; ++i){
        file << i*dt << " " << v[i]
             << " " << v_exact[i] << "\n";
    }
    file.close();

    return 0;
}