#include <iostream>
#include <cmath>
#include <stdlib.h>

using namespace std;
float f(float t,float y);
float EulerExplicite (float t0, float tf,float y0,int N, float(*func)(float,float));
float EulerImplicite(float xo,int N,float yo,float h,float t1,float(*funcf)(float,float,float,float),float(*funcg)(float,float,float,float));


float f(float t,float y){
	return -2*y+(exp(-2*t));
}

float f1 (float yi,float pas,float tiet1,float yiet1){
    float res;
    res= yiet1-(yi+pas*(-2*yiet1+(exp(-2*tiet1))));
    return res;
}
float g2(float yi,float pas,float tiet1,float yiet1){
    float res;
    res=1+2*pas;
    return res;
}

int main (void){
cout <<"resultat Euler explicite" << EulerExplicite(0.0,4.0,0.1,80,f)<<endl;
cout<<" res Euler implicite "<< EulerImplicite(0.11,80,0.1,0.005,0.1,f1,g2)<<endl;
}


float EulerExplicite (float to, float tf,float yo,int N, float(*func)(float,float)){
    float som=yo;
    float pas=(tf-to)/(N);
    for(int i = 0; i <N; i++){
       som=som+pas*func(to+i*pas,som);
    }
    return som;
}

float EulerImplicite(float x0,int N,float yo,float h,float t1,float(*funcf)(float,float,float,float),float(*funcg)(float,float,float,float)){
    int nbitermax=N;
    for(int i=0; i<=nbitermax;i++){
		x0= x0-funcf(yo,h,t1,x0)/funcg(yo,h,t1,x0);
    }
 	return x0;
}