#include <iostream>
#include <fstream>
using namespace std;
#define AMOUNT 1000
int main() { //явный метод эйлера. след. итерация вычисляется на основе пред. значения
	//одношаговый
	double a = 0.9, b = 0.1, h = 0.01, Y[AMOUNT];
	Y[0] = 1;
	ofstream file;
	file.open("zopka.txt", fstream::trunc);
	//4islennij
	//cout << "y_0: " << Y[0] << endl;
	for (int i = 1; i < AMOUNT; i++) {
		Y[i] = Y[i - 1] + h * (a * Y[i - 1] - b * pow(Y[i - 1], 2));
		if (AMOUNT == 1000) {
			if (i % 2 != 0) {
				//cout << "y_" << i << ": " << Y[i] << endl;
				file << Y[i] << endl;
			}
		}
		else {
			//cout << "y_" << i << ": " << Y[i] << endl;
			file << Y[i] << endl;
		}
	}
	int x = a / h;
	//cout << endl << "Result" << endl;
	//cout << endl << "Analyth y_" << x << " (t) = " << (Y[0] * a * exp(a * h)) / (a + b * Y[0] * (exp(a * h) - 1)) << endl;
	//cout << endl << "Euler method y_" << x << " (t) = " << Y[x] << endl<<endl;
	// analyth
	ofstream file1;
	file1.open("zopka2.txt", fstream::trunc);
	//cout << "y_0: " << Y[0] << endl;
	for (int j = 1; j < AMOUNT; j++) {

		Y[j] = (Y[0] * a * exp(a * h * j)) / (a + b * Y[0] * (exp(a * h * j) - 1));
		if (AMOUNT == 1000) {
			if (j % 2 != 0) {
				//cout << "y_" << j << ": " << Y[j] << endl;
				file1 << Y[j]  << endl;
			}
		}
		else {
			//cout << "y_" << j << ": " << Y[j] << endl;
			file1 << Y[j]  << endl;
		}
	}

	file.close();
	file1.close();
	system("PAUSE");
}

//метод ад.башфорда неявный, многошаговый