[NM] Ordinary Differential Equations

#include <iostream>
#include <cmath>
#include <vector>
#include <iomanip>
#include <sstream>
#include <fstream>

#define PI 3.1415926535897932384626433832795028841971
#define _E 2.71828182846
#define WIDTH 7
#define WIDTH_i 4
#define WIDTH_xi 5
#define WIDTH_f 15

#define MAX_X 2
#define START_X -15
#define STEP 0.2

using namespace std;

class Results
{
private:
    vector < vector < double > > results;

public:
    Results() {}
    ~Results() {}

    vector < vector < double > > get()
    {
        return results;
    }

    void set(vector < vector < double > > input)
    {
        results = input;
    }

    void pushLine(double x_i, double y_i, double f, double delta, double diff, double realV)
    {
        vector < double > tmp;
        tmp.push_back(x_i);
        tmp.push_back(y_i);
        tmp.push_back(f);
        tmp.push_back(delta);
        tmp.push_back(diff);
        tmp.push_back(realV);

        results.push_back(tmp);
    }

    vector < double > getLine(unsigned int i)
    {
        return results[i];
    }

    bool createCSVstr()
    {
        ofstream csv;
        csv.open("output.csv");
        if (!csv.is_open())
            return false;

        csv << "x;y;f(xy);delta;error;realV;\n";
        for (unsigned int i=0;i<results.size();++i)
        {
            for (unsigned int j=0;j<results[i].size();++j)
            {
                csv << results[i][j] << ";";
            }
            csv << "\n";
        }

        csv.close();
        return true;
    }
};

double f(double x, double y)
{
    return (y-10.0)/4.0 + 12.0*x*exp((5.0+x)/4.0);
}

double f1(double x)
{
    return (10.0 + 6.0*exp((5.0+x)/4.0)*x*x);
}

int main()
{
    const double interval = STEP;
    const double initialCondition = f1(START_X);

    stringstream buffer;
    buffer << "|" << setw(WIDTH_i) << "i" << "|"
        << setw(WIDTH_xi) << "x_i" << "|"
        << setw(WIDTH_f) << "y_i" << "|"
        << setw(WIDTH_f) << "f(x,y)" << "|"
        << setw(WIDTH_f) << "d y_i" << "|"
        << setw(WIDTH_f) << "Real v" << "|"
        << setw(WIDTH_f) << "Error" << "|\n";
    cout << buffer.str();
    for (unsigned int i=0;i<buffer.str().length()-1;++i)
        cout << "-";
    cout << "\n";

    unsigned int i=0;
    Results result;

    do
    {
        double x_i = START_X+i*interval;

        double y_i;
        if (i != 0)
            y_i = result.getLine(i-1).at(1)+result.getLine(i-1).at(3);
        else
            y_i = initialCondition;

        double f_i = f(x_i, y_i);
        double delta = interval*f_i;
        double realValue = f1(x_i);
        double diff = realValue - y_i;

        result.pushLine(x_i, y_i, f_i, delta, diff, realValue);

        buffer.str("");
        buffer << "|" << setw(WIDTH_i) << i << "|"
            << setw(WIDTH_xi) << x_i << "|"
            << setw(WIDTH_f) << y_i << "|"
            << setw(WIDTH_f) << f_i << "|"
            << setw(WIDTH_f) << delta << "|"
            << setw(WIDTH_f) << realValue << "|"
            << setw(WIDTH_f) << diff << "|\n";
        cout << buffer.str();
        ++i;
    } while((START_X+i*interval) <= MAX_X);

    if (result.createCSVstr())
        cout << "Results writen to file.\n";
    else
        cout << "File saving failed.\n";

    return 0;
}