import java.lang.Math;

 //maybe change the names of variables for the functions to make it less confusing?
public class RungeKutta {

	//change N, h and initial values according to what we need
	int N = 20;	/** number of steps */
	double h = 0.01; /** step size */
	double x0 = 0.0;		/** initial value */
	double v0 = 1.0;		/** initial value */
	double t[] = new double[N]; /** time after i-th step */
	double x[] = new double[N];
	double v[] = new double[N];

	public RungeKutta() {

		for(int i = 0; i < N; i++)
			t[i] = i;

		x[0] = x0;
		v[0] = v0;

		for(int j = 1; j < N; j++) {

			x[j] = 0;
			v[j] = 0;
		}
	}

	public double f1(double t1, double x1, double v1) {

		return v1;
	}

	//change this into our function
	public double f2(double t2, double x2, double v2) {

		return -v2 -Math.sin(x2) + Math.sin(t2);
	}

	public void rungeKutta() {

		double k1, k2, k3, k4;
		double l1, l2, l3, l4;

		for(int i = 0; i < (t.length-1); i++) {

			k1 = f1(t[i], x[i], v[i]);
			l1 = f2(t[i], x[i], v[i]);
			k2 = f1(t[i] + h/2, x[i] + h*k1/2, v[i] + h*l1/2);
			l2 = f2(t[i] + h/2, x[i] + h*k1/2, v[i] + h*l1/2);
			k3 = f1(t[i] + h/2, x[i] + h*k2/2, v[i] + h*l2/2);
			l3 = f2(t[i] + h/2, x[i] + h*k2/2, v[i] + h*l2/2);
			k4 = f1(t[i] + h, x[i] + h*k3, v[i] + h*k3);
			l4 = f2(t[i] + h, x[i] + h*k3, v[i] + h*k3);

			x[i+1] = x[i] + h/6*(k1 + 2*k2 + 2*k3 + k4);
			v[i+1] = v[i] + h/6*(l1 + 2*l2 + 2*l3 + l4);
			t[i+1] = t[i] + h;

		}

		for(int i = 0; i < t.length; i++)
			System.out.println("t = " + t[i] + ", x = " + x[i] + " , v = " + v[i]);
	}

	public static void main(String[] args) {

		RungeKutta RK = new RungeKutta();
		RK.rungeKutta();

	}

}