Data commit

Task/Runge-Kutta-method/C-sharp/runge-kutta-method.cs

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+using System;
+
+namespace RungeKutta
+{
+    class Program
+    {
+        static void Main(string[] args)
+        {
+            //Incrementers to pass into the known solution
+            double t = 0.0;
+            double T = 10.0;
+            double dt = 0.1;
+
+            // Assign the number of elements needed for the arrays
+            int n = (int)(((T - t) / dt)) + 1;
+
+            // Initialize the arrays for the time index 's' and estimates 'y' at each index 'i'
+            double[] y = new double[n];
+            double[] s = new double[n];
+
+            // RK4 Variables
+            double dy1;
+            double dy2;
+            double dy3;
+            double dy4;
+
+            // RK4 Initializations
+            int i = 0;
+            s[i] = 0.0;
+            y[i] = 1.0;
+
+            Console.WriteLine(" ===================================== ");
+            Console.WriteLine(" Beging 4th Order Runge Kutta Method ");
+            Console.WriteLine(" ===================================== ");
+
+            Console.WriteLine();
+            Console.WriteLine(" Given the example Differential equation: \n");
+            Console.WriteLine("     y' = t*sqrt(y) \n");
+            Console.WriteLine(" With the initial conditions: \n");
+            Console.WriteLine("     t0 = 0" + ", y(0) = 1.0 \n");
+            Console.WriteLine(" Whose exact solution is known to be: \n");
+            Console.WriteLine("     y(t) = 1/16*(t^2 + 4)^2 \n");
+            Console.WriteLine(" Solve the given equations over the range t = 0...10 with a step value dt = 0.1 \n");
+            Console.WriteLine(" Print the calculated values of y at whole numbered t's (0.0,1.0,...10.0) along with the error \n");
+            Console.WriteLine();
+
+            Console.WriteLine(" y(t) " +"RK4" + " ".PadRight(18) + "Absolute Error");
+            Console.WriteLine(" -------------------------------------------------");
+            Console.WriteLine(" y(0) " + y[i] + " ".PadRight(20) + (y[i] - solution(s[i])));
+
+            // Iterate and implement the Rk4 Algorithm
+            while (i < y.Length - 1)
+            {
+
+                dy1 = dt * equation(s[i], y[i]);
+                dy2 = dt * equation(s[i] + dt / 2, y[i] + dy1 / 2);
+                dy3 = dt * equation(s[i] + dt / 2, y[i] + dy2 / 2);
+                dy4 = dt * equation(s[i] + dt, y[i] + dy3);
+
+                s[i + 1] = s[i] + dt;
+                y[i + 1] = y[i] + (dy1 + 2 * dy2 + 2 * dy3 + dy4) / 6;
+
+                double error = Math.Abs(y[i + 1] - solution(s[i + 1]));
+                double t_rounded = Math.Round(t + dt, 2);
+
+                if (t_rounded % 1 == 0)
+                {
+                    Console.WriteLine(" y(" + t_rounded + ")" + " " + y[i + 1] + " ".PadRight(5) + (error));
+                }
+
+                i++;
+                t += dt;
+
+            };//End Rk4
+
+            Console.ReadLine();
+        }
+
+        // Differential Equation
+        public static double equation(double t, double y)
+        {
+            double y_prime;
+            return y_prime = t*Math.Sqrt(y);
+        }
+
+        // Exact Solution
+        public static double solution(double t)
+        {
+            double actual;
+            actual = Math.Pow((Math.Pow(t, 2) + 4), 2)/16;
+            return actual;
+        }
+    }
+}