Create Predictor-corrector-method.cpp

Fixes #2529 predictor-corrector method added

others/Predictor-corrector-method.cpp

@@ -0,0 +1,38 @@
+#include <iostream>
+#include <cmath>
+
+// Define the ODE function f(x, y)
+double f(double x, double y) {
+    return x - y; // Replace this with your desired ODE function
+}
+
+// Predictor-Corrector method to approximate the solution
+double predictorCorrector(double x0, double y0, double h, double x_target) {
+    double x = x0;
+    double y = y0;
+
+    while (x < x_target) {
+        // Predictor Step (Euler's Method)
+        double y_pred = y + h * f(x, y);
+
+        // Corrector Step (Improved Euler's Method)
+        y = y + 0.5 * h * (f(x, y) + f(x + h, y_pred));
+
+        x += h;
+    }
+
+    return y; // Approximate solution at x_target
+}
+
+int main() {
+    double x0 = 0.0;           // Initial value of x
+    double y0 = 1.0;           // Initial value of y
+    double h = 0.1;            // Step size (adjust as needed)
+    double x_target = 1.0;     // Target value of x for the solution
+
+    double result = predictorCorrector(x0, y0, h, x_target);
+
+    std::cout << "Approximate solution at x = " << x_target << ": y = " << result << std::endl;
+
+    return 0;
+}