added a few root finding algorithm in java

java/maths/RootFinding.java

@@ -0,0 +1,115 @@
+import java.util.function.Function;
+
+public class RootFinding {
+
+    /**
+     * Bisection method for finding the root of a function.
+     * 
+     * @param f       The function for which to find the root.
+     * @param a       The lower bound of the interval.
+     * @param b       The upper bound of the interval.
+     * @param epsilon The tolerance for convergence.
+     * @return The approximate root of the function.
+     */
+    public static double bisectionMethod(Function<Double, Double> f, double a, double b, double epsilon) {
+        if (f.apply(a) * f.apply(b) >= 0) {
+            throw new IllegalArgumentException("Function has the same signs at the endpoints.");
+        }
+
+        double c = a;
+        while ((b - a) / 2 > epsilon) {
+            c = (a + b) / 2;
+            if (f.apply(c) == 0.0) {
+                break;
+            } else if (f.apply(c) * f.apply(a) < 0) {
+                b = c;
+            } else {
+                a = c;
+            }
+        }
+        return c;
+    }
+
+    /**
+     * Secant method for finding the root of a function.
+     * 
+     * @param f       The function for which to find the root.
+     * @param x0      Initial guess.
+     * @param x1      Second guess.
+     * @param epsilon The tolerance for convergence.
+     * @return The approximate root of the function.
+     */
+    public static double secantMethod(Function<Double, Double> f, double x0, double x1, double epsilon) {
+        double x2 = x0;
+        while (Math.abs(x1 - x0) > epsilon) {
+            x2 = x1 - f.apply(x1) * (x1 - x0) / (f.apply(x1) - f.apply(x0));
+            x0 = x1;
+            x1 = x2;
+        }
+        return x2;
+    }
+
+    /**
+     * False Position method for finding the root of a function.
+     * 
+     * @param f       The function for which to find the root.
+     * @param a       The lower bound of the interval.
+     * @param b       The upper bound of the interval.
+     * @param epsilon The tolerance for convergence.
+     * @return The approximate root of the function.
+     */
+    public static double falsePositionMethod(Function<Double, Double> f, double a, double b, double epsilon) {
+        if (f.apply(a) * f.apply(b) >= 0) {
+            throw new IllegalArgumentException("Function has the same signs at the endpoints.");
+        }
+
+        double c = a; // Initialize c to a
+        while (Math.abs(b - a) > epsilon) {
+            c = a - f.apply(a) * (b - a) / (f.apply(b) - f.apply(a));
+            if (f.apply(c) == 0.0)
+                break;
+            else if (f.apply(c) * f.apply(a) < 0)
+                b = c;
+            else
+                a = c;
+        }
+        return c;
+    }
+
+    /**
+     * Fixed Point method for finding a root of the equation x = g(x).
+     * 
+     * @param g            The function g(x) such that x = g(x) at the root.
+     * @param initialGuess The initial guess for x.
+     * @param epsilon      The tolerance for convergence.
+     * @return The approximate fixed point of g.
+     */
+    public static double fixedPointMethod(Function<Double, Double> g, double initialGuess, double epsilon) {
+        double x0 = initialGuess;
+        double x1 = g.apply(x0);
+        while (Math.abs(x1 - x0) > epsilon) {
+            x0 = x1;
+            x1 = g.apply(x0);
+        }
+        return x1;
+    }
+
+    // Example usage
+    public static void main(String[] args) {
+        // Function to find root of x^2 - 2
+        Function<Double, Double> f = x -> x * x - 2;
+
+        // Using Bisection Method
+        System.out.println("Root found by Bisection Method: " + bisectionMethod(f, 0, 2, 0.001));
+
+        // Using Secant Method
+        System.out.println("Root found by Secant Method: " + secantMethod(f, 1, 2, 0.001));
+
+        // Using False Position Method
+        System.out.println("Root found by False Position Method: " + falsePositionMethod(f, 0, 2, 0.001));
+
+        // Using Fixed Point Method
+        Function<Double, Double> g = x -> Math.sqrt(2); // Example function for fixed point
+        System.out.println("Root found by Fixed Point Method: " + fixedPointMethod(g, 1, 0.001));
+    }
+}