/*	File:	RK45.cpp



			Christer Karlsson



This code implements The Runge-Kutta method

to solve Ordinary Differential Equations.



    Allowed inputs are real numbers (long double).

    Define f in the function procedure    */



#include <iostream>

#include <cmath>

#include <iomanip>		// Needed too manipulate the display



using namespace std;





// the function

long double f(long double t,long double x)

{

    long double f;

    f=sqrt(1+pow(t,3));

    return f;

}



// The Runge-Kutta method of order 4 function

void RK45(long double h, long double t, long double x, int n)

{

    int j;

    long double K1, K2, K3, K4, ta;



    cout << 0 << '\t' << t << "\t\t" << x << endl;

    ta=t;

    for (j=1; j<=n; j++)

    {

        K1=h*f(t,x);

        K2=h*f((t+h/2),(x+K1/2));

        K3=h*f((t+h/2),(x+K2/2));

        K4=h*f((t+h),(x+K3));

        x=x+(K1+2*K2+2*K3+K4)/6;

        t=ta+j*h;

        cout << j << '\t' << t << "\t\t" << x << endl;

    }

}

int main(int argc, char *argv[])

{

    int n=36, digits=13;

    long double a=0, b=1, x=0;

    long double h, t;



    h=(b-a)/n;

    t=a;

    // Set a fixed amount of digits to show

    cout.setf(ios::fixed );

    cout.setf(ios::showpoint);

    cout <<  setprecision(digits);



    // Call the integrating function

    RK45(h, t, x, n);



    // Unset the fixed point

    cout.unsetf(ios::fixed);

    cout.unsetf(ios::showpoint);



    cout << endl;

    system("PAUSE");

    return 0;

}