Тест 4 "ур-е Гельмгольца" (внут. сфера) (старая формула)

#include "pch.h"
#include <iostream>
#include <conio.h>
#include <string>
#include <cstring>
#include <math.h>
#include <cstdlib>
#include <ctime>
#include <cmath>
#include <complex>
using namespace std;

int main()
{
    int M = 100, N = 100;
    complex< double> V0;
    long double K0 = 0, S0 = 0;
    const double pi = 3.14159265358979;
    double x1, x2, x3, x, y1, y2, y3, y11, y21, y31, h = 2.0 * pi / N, H = pi / (1.0 * M), etta, xminusy, R;
    double A = N * h, B = M * H;
    double tetta, betta, y1pr, y2pr, y3pr;
    double uq = pi / (1.0 * N), vl = pi / (2.0 * M);
    complex< double > z(0, 1.0); // мнимая единица
    complex< double > z1(1.0, 0);
    for (int i = 1; i < 6; i++)
    {
        R = 1 - pow(10, (-1)*i);
        cout << "R=" << R << endl;
        y11 = sin(vl)*cos(uq);
        y21 = sin(vl)*sin(uq);
        y31 = cos(vl);
        x1 = y11 * R;
        x2 = y21 * R;
        x3 = y31 * R;
        cout << "x1=" << x1 << endl;
        cout << "x2=" << x2 << endl;
        cout << "x3=" << x3 << endl;
        x = pow(pow(x1, 2) + pow(x2, 2) + pow(x3, 2), 0.5);
        cout << "x=" << x << endl;
        // Вычисление K0
        for (int m = 0; m < M; m++)
        {
            double vm = (m + 0.5)*H;
            for (int n = 0; n < N; n++)
            {
                double un = (n + 0.5)*h;
                y1 = sin(vm)*cos(un);
                y2 = sin(vm)*sin(un);
                y3 = cos(vm);
                etta = sin(vm);
                xminusy = pow(pow(x1 - y1, 2) + pow(x2 - y2, 2) + pow(x3 - y3, 2), 0.5);
                K0 = K0 + ((h * H * etta * 1.0  * cos(vm) / xminusy) / (4 * pi));
            }
        }
        // Вычисление S0
        /* for (int m = 0; m < M; m++)
        {
            double vm = (m + 0.5)*H;
            for (int n = 0; n < N; n++)
            {
                double un = (n + 0.5)*h;
                y1pr = cos(un) * cos(vm);
                y2pr = sin(un) * cos(vm);
                y3pr = (-1)*sin(vm);
                betta = sqrt(pow(y1pr, 2) + pow(y2pr, 2) + pow(y3pr, 2));

                // Вычисление I(H)






                tetta = 1.0 / betta;
                y1 = sin(vm)*cos(un);
                y2 = sin(vm)*sin(un);
                y3 = cos(vm);
                etta = sin(vm);
                xminusy = pow(pow(x1 - y1, 2) + pow(x2 - y2, 2) + pow(x3 - y3, 2), 0.5);
                S0 = S0 + (etta * tetta);
            }
        } */

        cout << "K0=" << K0 << endl;
        if (abs(x) < 1)
        {
            V0 = (z - z1) * exp(z) * cos(x3 / R) * (abs(x) * cos(abs(x)) - sin(abs(x))) / pow(abs(x),2);
        }
        else if (abs(x) > 1)
        {
            V0 = (cos(1) - sin(1)) * cos(x3 / R) * (z * abs(x) - z1) / pow(abs(x), 2);
        }

        cout << "V0=" << abs(V0) << endl;
        cout << "______________________" << endl;
    }

    return 0;
}






#include "pch.h"
#include <iostream>
#include <conio.h>
#include <string>
#include <cstring>
#include <math.h>
#include <cstdlib>
#include <ctime>
#include <cmath>
#include <algorithm>
#include <complex>
using namespace std;

int main()
{
    int M = 50, N = 50;
    complex <double> V1;
    complex <double> K1;
    complex <double> p(0, 0);
    const double pi = 3.14159265358979;
    double x1, x2, x3, x, y1, y2, y3, y11, y21, y31, h = 2.0 * pi / N, H = pi / (1.0 * M), etta, xminusy, R;
    double A = N * h, B = M * H;
    //double tetta, betta, y1pr, y2pr, y3pr;
    // double uq = pi / (1.0 * N), vl = pi / (2.0 * M);
    complex <double> z(0, 1.0); // мнимая единица
    complex< double > z1(1.0, 0);
    setlocale(LC_ALL, "Rus");
    for (int i = 1; i < 6; i++)
    {
        R = 1 - pow(10, (-1)*i);
        cout << "R=" << R << endl;
        for (int q = 0; q <= 2 * N; q++)
        {
            double uq = pi * q / (1.0 * N);
            for (int l = 0; l <= 2 * M; l++)
            {
                double vl = pi * l / (2.0 * M);
                y11 = sin(vl)*cos(uq);
                y21 = sin(vl)*sin(uq);
                y31 = cos(vl);
                x1 = y11 * R;
                x2 = y21 * R;
                x3 = y31 * R;
                //cout << "x1=" << x1 << endl;
                //cout << "x2=" << x2 << endl;
                //cout << "x3=" << x3 << endl;
                x = pow(pow(x1, 2) + pow(x2, 2) + pow(x3, 2), 0.5);
                //cout << "x=" << x << endl;
                // Вычисление K1
                for (int m = 0; m < M; m++)
                {
                    double vm = (m + 0.5)*H;
                    for (int n = 0; n < N; n++)
                    {
                        double un = (n + 0.5)*h;
                        y1 = sin(vm)*cos(un);
                        y2 = sin(vm)*sin(un);
                        y3 = cos(vm);
                        etta = sin(vm);
                        xminusy = pow(pow(x1 - y1, 2) + pow(x2 - y2, 2) + pow(x3 - y3, 2), 0.5);
                        K1 = K1 + ((h * H * etta * 1.0 * exp(z * xminusy) * cos(vm) / xminusy) / (4 * pi));
                    }
                }
                if (abs(x) < 1)
                {
                    V1 = (z - z1) * exp(z) * x3 * (abs(x) * cos(abs(x)) - sin(abs(x))) / ( R * pow(abs(x), 2));
                }
                else if (abs(x) > 1)
                {
                    V1 = (cos(1) - sin(1)) * x3 * (z * abs(x) - z1) * exp(z * abs(x)) / ( R * pow(abs(x), 2));
                }

                complex <double> maximum = max(abs(p), abs(K1 - V1));
                K1 = 0;
                p = maximum;
            }
        }

        cout << "Абсолютная погрешность=" << abs(p) << endl;
        //cout << "V1=" << abs(V1) << endl;
        cout << "______________________" << endl;
    }

    return 0;
}