1 / modeling

#include <iostream>

int const n = 50, n1 = 40, m = n / n1;
double f1(double t, double x, double y, double z);
double f2(double t, double x, double y, double z);
double f3(double t, double x, double y, double z);
int main() {
    int i, k, ll;
    double k11, k12, k13, k21, k22, k23, k31, k32, k33, k14, k24, k34;
    double x, y, z, max;
    double res[11][n1 + 1], h, a, b, t, pi, xn, yn, zn;
    max = 1000.0;
    x = 3.0;
    y = -2.0;
    z = -3.0;
    a = 0.0;
    b = 1.0;
    h = (b - a) / double(n);
    k = 0;
    t = a;
    res[0][0] = t;
    res[1][0] = x;
    res[2][0] = y;
    res[3][0] = z;
    for (i = 1; i <= n; i++) {
        k11 = f1(t, x, y, z);
        k21 = f2(t, x, y, z);
        k31 = f3(t, x, y, z);
        k12 = f1(t + h / 2.0, x + h * k11 / 2.0, y + h * k21 / 2.0, z + h * k31 / 2.0);
        k22 = f2(t + h / 2.0, x + h * k11 / 2.0, y + h * k21 / 2.0, z + h * k31 / 2.0);
        k32 = f3(t + h / 2.0, x + h * k11 / 2.0, y + h * k21 / 2.0, z + h * k31 / 2.0);
        k13 = f1(t + h / 2.0, x + h * k12 / 2.0, y + h * k22 / 2.0, z + h * k32 / 2.0);
        k23 = f2(t + h / 2.0, x + h * k12 / 2.0, y + h * k22 / 2.0, z + h * k32 / 2.0);
        k33 = f3(t + h / 2.0, x + h * k12 / 2.0, y + h * k22 / 2.0, z + h * k32 / 2.0);
        k14 = f1(t + h, x + h * k13, y + h * k23, z + h * k33);
        k24 = f2(t + h, x + h * k13, y + h * k23, z + h * k33);
        k34 = f3(t + h, x + h * k13, y + h * k23, z + h * k33);
        x = x + h * (k11 + 2.0 * (k12 + k13) + k14) / 6.0;
        y = y + h * (k21 + 2.0 * (k22 + k23) + k24) / 6.0;
        z = z + h * (k31 + 2.0 * (k32 + k33) + k34) / 6.0;
        t = t + h;
        if (i % m == 0) {
            k = k + 1;
            res[0][k] = t;
            res[1][k] = x;
            res[2][k] = y;
            res[3][k] = z;
            res[4][k] = exp(t) + exp(2.0 * t) + exp(-t);
            res[5][k] = exp(t) - 3.0 * exp(-t);
            res[6][k] = exp(t) + exp(2.0 * t) - 5.0 * exp(-t);
            res[7][k] = res[4][k] - res[1][k];
            res[8][k] = res[5][k] - res[2][k];
            res[9][k] = res[6][k] - res[3][k];
        }
        if (res[7][k] < 0.0) {
            res[7][k] = -res[7][k];
        }
        else if (res[8][k] < 0.0) {
            res[8][k] = -res[8][k];
        }
        else if (res[9][k] < 0.0) {
            res[9][k] = -res[9][k];
        }
        res[10][k] = res[7][k] + res[8][k] + res[9][k];
    }
    ll = k;
    printf("k=%d\n", ll);
    for (i = 0; i <= ll; i++) {
        if (res[10][i] < max)
            max = res[10][i];
    }
    for (i = 0; i <= n1; i++) {
        printf("t=%.16lf\n", res[0][i]);
        printf("x=%.16lf x(exact)=%.16lf delta=%.16lf\n", res[1][k], res[4][k], res[1][k] - res[4][k]);
        printf("y=%.16lf y(exact)=%.16lf delta=%.16lf \n", res[2][k], res[5][k], res[2][k] - res[5][k]);
        printf("z=%.16lf z(exact)=%.16lf delta=%.16lf \n", res[3][k], res[6][k], res[3][k] - res[6][k]);
    }
    printf("result:\n");
    printf("t=%.16lf\n", res[0][n1]);
    printf("x=%.16lf x(exact)=%.16lf delta=%.16lf\n", res[1][n1], res[4][n1], res[1][n1] - res[4][n1]);
    printf("y=%.16lf y(exact)=%.16lf delta=%.16lf \n", res[2][n1], res[5][n1], res[2][n1] - res[5][n1]);
    printf("z=%.16lf z(exact)=%.16lf delta=%.16lf \n", res[3][n1], res[6][n1], res[3][n1] - res[6][n1]);
    printf("max norma|x|1=%.16lf \n", max / 3.0);
}
double f1(double t, double x, double y, double z) {
    return x + z - y;
}
double f2(double t, double x, double y, double z) {
    return x + y - z;
}
double f3(double t, double x, double y, double z) {
    return 2.0 * x - y;
}