Euler’s method for a first-order ODE

• Time : $O(nb)$
• Space : $O(1)$

#include <bits/stdc++.h>
using namespace std;
class EulerOde
{
public:
    static double exact_sol(double t){
        return  1.0 + 0.5*std::exp(-4.0*t) - 0.5*std::exp(-2.0*t);
    }

    static double f(double y, double t){
        return 2.0 - std::exp(-4.0*t) - 2.0*y;
    }

    static double exEuler(int nb){

        double y = 1, t = 0, h = 1. / nb;
        double error = std::fabs(y - exact_sol(t))/exact_sol(t);

        for(int i=0; i < nb; i++){
            y += f(y,t)*h;
            t += h;
            error += std::fabs(y - exact_sol(t))/exact_sol(t);
        }

        return std::trunc((error/(nb+1.0f))*1e6f)/1e6f;
    }
};