/*     Example Three
         Example of the use of the class RungeKutta demonstrating the use of the
         instance methods in solving a single ordinary differential equation:
                  dy/dx = a.x.sqrt(1.0 - y*y)

       Michael Thomas Flanagan
       m.flanagan@ee.ucl.ac.uk

       Updated  January 2010
*/

import flanagan.integration.*;

// Class to demonstrate the fourth order Runge-Kutta method in class RungeKutta.
public class RungeKuttaExampleThree{

         public static void main(String[ ] arg){

                  // Create instance of the class holding the derivative evaluation method
                  Deriv d1 = new Deriv();

                  // Assign values to constants in the derivative function
                  double a = 10.0D;
                  d1.setA(a);

                  // Variable declarations
                  double x0 = 0.0D;      // initial value of x
                  double y0 = 0.0D;      // initial value of y
                  double xn = 1.0D;      // final value of x
                  double yn = 0.0D;      // returned value of y at x = xn
                  double h = 0.01D;      // step size

                  // Create an instance of RungeKutta
                  RungeKutta rk = new RungeKutta();

                  // Set values needed by fixed step size method
                  rk.setInitialValueOfX(x0);
                  rk.setFinalValueOfX(xn);
                  rk.setInitialValuesOfY(y0);
                  rk.setStepSize(h);

                  // Call Fourth Order Runge-Kutta method
                  yn = rk.fourthOrder(d1);

                  // Output the result
                  System.out.println("Fourth order Runge-Kutta procedure");
                  System.out.println("The value of y at x = " + xn + " is " + yn);
                  System.out.println("Number of iterations = " + rk.getNumberOfIterations());

                   // Set additional values needed by fixed step size method
                  rk.setToleranceScalingFactor(1e-5);
                  rk.setToleranceAdditionFactor(1e-3);

                  // Call Fehlberg-Runge-Kutta method
                  yn = rk.fehlberg(d1);

                  // Output the result
                  System.out.println("\nFehlberg-Runge-Kutta procedure");
                  System.out.println("The value of y at x = " + xn + " is " + yn);
                  System.out.println("Number of iterations = " + rk.getNumberOfIterations());

                  // Call Cash-Karp-Runge-Kutta method
                  yn = rk.cashKarp(d1);

                  // Output the result
                  System.out.println("\nCash-Karp-Runge-Kutta procedure");
                  System.out.println("The value of y at x = " + xn + " is " + yn);
                  System.out.println("Number of iterations = " + rk.getNumberOfIterations());
         }
}


// Class to evaluate the derivative dy/dx = a.x.sqrt(1.0 + y*y) for given values of x and y.
class Deriv implements DerivFunction{

        private double a = 0.0D;

        public double deriv(double x, double y){
                double dydx = a*x*Math.sqrt(1.0 + y*y);
                return dydx;
        }

        public void setA(double a){
                this.a = a;
        }
}