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

#define M_E 2.71828f

// Return the value of the function for the given input
float Part1Function(float t, float x)
{
	// Return the value from
	return sin(pow(M_E, t)) * pow(x, 2);
}


// Run the runge-kutta on the function given the h provided
void Runge_KuttaPart1Function(float h)
{
	float k1, k2, k3, start_t, end_t, start_x;

	start_t = 0.0f;
	start_x = 1.0f;
	end_t = 3.0f;

	// Print out the table headers
	cout << "tn \t k1 \t k2 \t k3 \t xn \n";

	// Print out the first line of the table with the initial values
	cout << start_t << "\t\t\t\t\t" << start_x << "\n";

	// Move to the first iteration
	start_t += h;

	// Iterate through each h value and output the results
	for(start_t; start_t != end_t;start_t += h)
	{
		// Calculate k1, k2, k3
		k1 = h * Part1Function(start_t, start_x);
		k2 = h * Part1Function((start_t + (h/2.0f)), (start_x + (k1/2.0f)));
		k3 = h * Part1Function((start_t + h), ((start_x - k1)+(2.0f * k2)));

		// Calculate the next y
		start_x = start_x + ((1.0f/6.0f) * k1) + ((2.0f/3.0f) * k2) + ((1.0f/6.0f) * k3);

		// Now print out this line of calculations
		cout << start_t << "\t" << k1 << "\t" << k2 << "\t" << k3 << "\t" << start_x  << "\n";
	}
}

// Run the test on the various values of h for the first assignment
void main()
{
	// Run Runge_KuttaPart1Function for each h in part 1
	Runge_KuttaPart1Function(1.0f);
}