NM_Lab7

#include <iostream>
#include <fstream>
#include <iomanip>
#include <math.h>

using namespace std;

using std::setw;
ofstream out;
double H;
double n;

double f(double x)
{
    return -sqrt(pow(x,2)*sqrt(12*pow(x,2)+9)-3*x*x)/sqrt(2);
}

double df(double x, double y)
{
    return (3*pow(y,3)+6*y*x*x)/(2*x*y*y+3*pow(x,3));
}

double RungeKuttaStep(double x0, double y0)
{
    double f1,f2,f3,f4;
    f1=df(x0,y0);
    f2=df(x0+H/2,y0+H/2*f1);
    f3=df(x0+H/2,y0+H/2*f2);
    f4=df(x0+H,y0+H*f3);
    y0+=H/6*(f1+2*f2+2*f3+f4);
    return y0;
}

void RungeKutta(double x0, double y0)
{
    double e=0;
    printf("x0 \t y0 \t f(x0) \t |y0-f(x0)|\n");
    for(int i=0; i<1/H; i++){
        y0 = RungeKuttaStep(x0,y0);
        x0 += H;
        out << x0 << " " << y0 << " " << f(x0) << " " << fabs(y0-f(x0)) << endl;
        cout << setw(4) << x0 << " " << setw(8) << y0 << " " << setw(8) << f(x0) << " " << setw(13) << fabs(y0-f(x0)) << endl;
        if(e<fabs(y0-f(x0)))
           e=fabs(y0-f(x0));
    }
    out << "max|ei| " << e << endl;
    cout << "max|ei| " << e << endl;
}

void Adams(double x0, double y0)
{
    double k[4];
    double e=0;
    k[0]=df(x0,y0);
    printf("x0 \t y0 \t f(x0) \t |y0-f(x0)|\n");
    for(int i=1; i<4; i++){
        y0=RungeKuttaStep(x0,y0);
        x0+=H;
        k[i]=df(x0,y0);
        out << x0 << " " << y0 << " " << f(x0) << " " << fabs(y0-f(x0)) << endl;
        cout << setw(4) << x0 << " " << setw(8) << y0 << " " << setw(8) << f(x0) << " " << setw(13) << fabs(y0-f(x0)) << endl;
    }
    for(int i=3; i<1/H; i++)
    {
        y0+=H/24*(55*k[3]-59*k[2]+37*k[1]-9*k[0]);
        x0+=H;
        for(int j=0; j<3; j++)
        {
            k[j]=k[j+1];
        }
        k[3]=df(x0,y0);
        if(e<fabs(y0-f(x0)))
           e=fabs(y0-f(x0));
        out << x0 << " " << y0 << " " << f(x0) << " " << fabs(y0-f(x0)) << endl;
        cout << setw(4) << x0 << " " << setw(8) << y0 << " " << setw(8) << f(x0) << " " << setw(13) << fabs(y0-f(x0)) << endl;
    }
    out << "max|ei| " << e << endl;
    cout << "max|ei| " << e << endl;
}

int main()
{
    n=1024;
    out.open("Output.txt");
    for(int i=1; i<11; i++){
        H=1/n;
        n/=2;
        out << "H: " << H << endl;
        cout << "R-K:" << endl;
        RungeKutta(6,-18);
        cout << "Adams:" << endl;
        Adams(6,-18);
        cout << "***************************************" << endl;
    }
    out.close();
    return 0;
}