AntiKonuhov

/*Метод Эйлера*/
#include <iostream>
#include <fstream>
#include <string>
#include <iomanip>
using namespace std;

void priblizhennoe(ofstream&out, double N, double h, double t0, double U0)
{
    double t, u, f;
    t = t0;
    u = U0;
    //cout << "При t" << 0 << " = " << t << " U" << 0 << " = " << u << "\n";
    out << u << "\n";
    for (int i = 0; i < N; i++)
    {
        f = (4 / (t * t)) - (u / t) - (u * u);
        u = u + h * f;
        t = t + h;
        //cout << "При t" << i + 1 << " = " << t << " U" << i+1 << " = " << u << "\n";
        out << fixed << u << "\n";
    }
}
void tochnoe(ofstream&out, double N, double h, double t0, double U0, double C)
{
    double t, u;
    t = t0;
    u = U0;
    //cout << "При t" << 0 << " = " << t << " U" << 0 << " = " << u << "\n";
    out << setprecision(16);
    out << u << "\n";
    for (int i = 0; i < N; i++)
    {
        t = t + h;
        u = (2 * (t * t * t * t + C)) / (t * (t * t * t * t - C));
        //cout << "При t" << i + 1 << " = " << t << " U" << i+1 << " = " << u << "\n";
        out << u << "\n";
    }
}
int main()
{

    ofstream out("pribresh.txt");
    ofstream outt("tochnoee.txt");
    setlocale(LC_ALL, "RU");
    double t0, T, h, N, U0;
    cout << "Введите область [to,T]:\n";
    cin >> t0 >> T;
    cout << "Введите N и U0: ";
    cin >> N >> U0;
    h = (T - t0) / N;
    double C;
    C = (t0 * t0 * t0 * t0 * (t0 * U0 - 2)) / (2 + U0 * t0);
    //cout << "Приближенные решения: \n";
    priblizhennoe(out, N, h, t0, U0);
    //cout << "Точные решения: \n";
    tochnoe(outt, N, h, t0, U0, C);
    out.close();
    outt.close();
    ifstream inout("pribresh.txt");
    ifstream inoutt("tochnoee.txt");
    ofstream outn100("n100.txt");
    ofstream outtn100("tochn100.txt");
    string s, s1;
    while (inout.peek() != EOF)
    {
        inout >> s;
        inoutt >> s1;
        for (int i = 0; i < s.length(); i++)
        {
            if (s[i] == '.')
                s[i] = ',';
            if (s1[i] == '.')
                s1[i] = ',';
        }
        outn100 << s << "\n";
        outtn100 << s1 << "\n";
    }
    inout.close();
    inoutt.close();
    outn100.close();
    outtn100.close();

    return 0;
}
/*Метод Рунге-Кутта*/
#include <iostream>
#include <fstream>
#include <string>
#include <iomanip>
using namespace std;

double function(double t, double u)
{
    return 4 / (t * t) - (u / t) - (u * u);
}
void priblizhennoe(ofstream&out, double h, double N, double t0, double U0)
{
    double t, u, f, k1, k2, k3, k4;
    u = U0;
    t = t0;
    //cout << "Для t0 = " << t << " U0 = " << u << "\n";
    out << setprecision(16);
    out << u << "\n";
    for (int i = 0; i < N; i++)
    {
        k1 = function(t, u);
        k2 = function(t + h / 2, u + (h * k1) / 2);
        k3 = function(t + h / 2, u + (h * k2) / 2);
        k4 = function(t + h, u + h * k3);
        u += h * (k1 + (2 * k2) + (2 * k3) + k4) / 6;
        t += h;
        //cout << "При t" << i + 1 << " = " << t << " U" << i + 1 << " равно: " << u << "\n";
        out << u << "\n";
    }
}
void tochnoe(double N, double h, double t0, double U0, double C)
{
    double t, u;
    t = t0;
    u = U0;
    cout << "При t" << 0 << " = " << t << " U" << 0 << " = " << u << "\n";
    for (int i = 0; i < N; i++)
    {
        t = t + h;
        u = (2 * (t * t * t * t + C)) / (t * (t * t * t * t - C));
        cout << "При t" << i + 1 << " = " << t << " U" << i + 1 << " = " << u << "\n";
    }
}
int main()
{
    ofstream out("pribresh.txt");
    setlocale(LC_ALL, "RU");
    double t0, T, h, N, U0;
    cout << "Введите область [to,T]:\n";
    cin >> t0 >> T;
    cout << "Введите N и U0: ";
    cin >> N >> U0;
    h = (T - t0) / N;
    //double C;
    //C = (t0 * t0 * t0 * t0 * (t0 * U0 - 2)) / (2 + U0 * t0);
    //cout << "Приближенные решения: \n";
    priblizhennoe(out, h, N, t0, U0);
    out.close();
    //cout << "Точные решения: \n";
    //tochnoe(N, h, t0, U0);
    ifstream inout("pribresh.txt");
    ofstream outn100("n100.txt");
    string s;
    while (inout.peek() != EOF)
    {
        inout >> s;
        for (int i = 0; i < s.length(); i++)
            if (s[i] == '.')
                s[i] = ',';
        outn100 << s << "\n";
    }
    inout.close();
    outn100.close();

    return 0;
}
/*Метод посл. приближений*/
#include <iostream>
#include <fstream>
#include <string>
#include <iomanip>
#define EPS 0.000001
using namespace std;
double f(double t, double u)
{
    return 4 / (t * t) - u / t - (u * u);
}
void pribl(ofstream&out, double U0, double t0, int N, double h)
{
    double u, un, uo, t, tnext;
    bool a;
    int maxl = 1, l; //макс кол-во итераций
    uo = u = U0;
    t = t0;
    out << setprecision(16);
    out << u << "\n";
    //cout << "При t" << 0 << " = " << t << " U" << 0 << " = " << u << "\n";
    for (int i = 0; i < N; i++)
    {
        tnext = t + h;
        un = u + h * (f(t, u) + f(tnext, uo)) / 2;
        a = true;
        l = 1;
        while (abs(un - uo) > EPS)
        {
            uo = un;
            un = u + h * (f(t, u) + f(tnext, uo)) / 2;
            a = false;
            l++;
        }
        if (l > maxl)
            maxl = l;
        if (a)
            u = un;
        else
            u = uo;
        t = tnext;
        //cout << "При t" << i + 1 << " = " << t << " U" << i + 1 << " = " << u << "\n";
        out << u << "\n";
    }
    out << "Макс кол-во итераций = " << maxl;
}
void tochnoe(double N, double h, double t0, double U0, double C)
{
    double t, u;
    t = t0;
    u = U0;
    cout << "При t" << 0 << " = " << t << " U" << 0 << " = " << u << "\n";
    for (int i = 0; i < N; i++)
    {
        t = t + h;
        u = (2 * (t * t * t * t + C)) / (t * (t * t * t * t - C));
        cout << "При t" << i + 1 << " = " << t << " U" << i + 1 << " = " << u << "\n";
    }
}
int main()
{
    setlocale(LC_ALL, "RU");
    double t0, T, h, U0;
    int N;
    cout << "Введите область [to,T]:\n";
    cin >> t0 >> T;
    cout << "Введите N и U0: ";
    cin >> N >> U0;
    h = (T - t0) / N;
    double C;
    C = (t0 * t0 * t0 * t0 * (t0 * U0 - 2)) / (2 + U0 * t0);
    ofstream out("pribresh.txt");
    //cout << "Приближенные решения:\n";
    pribl(out, U0, t0, N, h);
    //cout << "\n";
    //cout << "Точные решения:\n";
    //tochnoe(N, h, t0, U0);
    out.close();
    ifstream in("pribresh.txt");
    ofstream outn("n100.txt");
    string s;
    while (in.peek() != EOF)
    {
        in >> s;
        for (int i = 0; i < s.length(); i++)
            if (s[i] == '.')
                s[i] = ',';
        outn << s << "\n";
    }
    in.close();
    outn.close();
    return 0;

}
/*Метод предиктор-корректор*/
#include <iostream>
#include <fstream>
#include <string>
#include <iomanip>
using namespace std;

double f(double t, double u)
{
    return 4 / (t * t) - u / t - (u * u);
}
void pribl(ofstream&out, double u0, double t0, double h, int N)
{
    double ue, u, t, tnext;
    u = u0;
    t = t0;
    //cout << "При t" << 0 << " = " << t << " U" << 0 << " = " << u << "\n";
    out << setprecision(16);
    out << u << "\n";
    for (int i = 0; i < N; i++)
    {
        ue = u + h * f(t, u);
        tnext = t + h;
        u = u + h * (f(t, u) + f(tnext, ue)) / 2;
        t = tnext;
        //cout << "При t" << i + 1 << " = " << t << " U" << i + 1 << " = " << u << "\n";
        out << u << "\n";
    }
}
void tochnoe(double N, double h, double t0, double U0, double C)
{
    double t, u;
    t = t0;
    u = U0;
    cout << "При t" << 0 << " = " << t << " U" << 0 << " = " << u << "\n";
    for (int i = 0; i < N; i++)
    {
        t = t + h;
        u = (2 * (t * t * t * t + C)) / (t * (t * t * t * t - C));
        cout << "При t" << i + 1 << " = " << t << " U" << i + 1 << " = " << u << "\n";
    }
}
int main()
{
    setlocale(LC_ALL, "RU");
    double t0, T, h, U0;
    int N;
    cout << "Введите область [to,T]:\n";
    cin >> t0 >> T;
    cout << "Введите N и U0: ";
    cin >> N >> U0;
    h = (T - t0) / N;
    double C;
    C = (t0 * t0 * t0 * t0 * (t0 * U0 - 2)) / (2 + U0 * t0);
    ofstream out("pribresh.txt");
    //cout << "Приближенные решения:\n";
    pribl(out, U0, t0, h, N);
    //cout << "\n";
    //cout << "Точные решения:\n";
    //tochnoe(N, h, t0, U0);
    out.close();
    ifstream in("pribresh.txt");
    ofstream outn("n100.txt");
    string s;
    while (in.peek() != EOF)
    {
        in >> s;
        for (int i = 0; i < s.length(); i++)
            if (s[i] == '.')
                s[i] = ',';
        outn << s << "\n";
    }
    in.close();
    outn.close();

    return 0;
}
/*Метод Ньютона*/
#include <iostream>
#include <fstream>
#include <string>
#include <iomanip>
#define eps 0.000001
using namespace std;

double f(double t, double u)
{
    return 4 / (t * t) - u / t - u * u;
}
double df(double t, double u)
{
    return -1 / t - 2 * u;
}
double F(double t, double y, double x, double h)
{
    return x - y - (h / 2) * (f(t, y) + f(t + h, x));
}
double dF(double t, double x, double h)
{
    return 1 - (h / 2) * df(t + h, x);
}
void priblizhennoe(ofstream&out, double t0, double U0, double h, int N)
{
    double y, t, x_prev, x_curr;
    y = U0;
    t = t0;
    bool a;
    int l, maxl = 1;
    //cout << "При t" << 0 << " = " << t << " U" << 0 << " = " << y << "\n";
    out << setprecision(16);
    out << y << "\n";
    for (int i = 0; i < N; i++)
    {
        x_curr = 0;
        x_prev = t;
        a = true;
        l = 0;
        while (a)
        {
            x_curr = x_prev - F(t, y, x_prev, h) / dF(t, x_prev, h);
            l++;
            if (abs(x_curr - x_prev) < eps)
                a = false;
            x_prev = x_curr;
        }
        t += h;
        y = x_curr;
        if (l > maxl)
            maxl = l;
        //cout << "При t" << i + 1 << " = " << t << " U" << i + 1 << " = " << y << "\n";
        out << y << "\n";
    }
    out << "Макс кол-во итераций = " << maxl;
}
void tochnoe(int N, double h, double t0, double U0, double C)
{
    double t, u;
    t = t0;
    u = U0;
    cout << "При t" << 0 << " = " << t << " U" << 0 << " = " << u << "\n";
    for (int i = 0; i < N; i++)
    {
        t = t + h;
        u = (2 * (t * t * t * t + C)) / (t * (t * t * t * t - C));
        cout << "При t" << i + 1 << " = " << t << " U" << i + 1 << " = " << u << "\n";
    }
}
int main()
{
    setlocale(LC_ALL, "RU");
    double t0, T, U0, h;
    int N;
    cout << "Введите t0 и T: \n";
    cin >> t0 >> T;
    cout << "Введите N и U0: \n";
    cin >> N >> U0;
    h = (T - t0) / N;
    double C;
    C = (t0 * t0 * t0 * t0 * (t0 * U0 - 2)) / (2 + U0 * t0);
   // cout << "Приближенные решения: \n";
    ofstream out("pribresh.txt");
    priblizhennoe(out, t0, U0, h, N);
    //cout << "\n";
   // cout << "Точные решения: \n";
    //tochnoe(N, h, t0, U0);
    out.close();
    ifstream in("pribresh.txt");
    ofstream outn("n100.txt");
    string s;
    while (in.peek() != EOF)
    {
        in >> s;
        for (int i = 0; i < s.length(); i++)
            if (s[i] == '.')
                s[i] = ',';
        outn << s << "\n";
    }
    in.close();
    outn.close();

    return 0;
}