How can I implement numerical methods in C++?

How can I implement numerical methods in C++?

You can start by using libraries like Eigen or implementing algorithms like Newton's method. What specific method are you interested in?

I'm interested in the Runge-Kutta method for solving ODEs.

Great choice! The Runge-Kutta method is widely used. Would you like a code example or an explanation of the algorithm?

A code example would be helpful.

Sure! Here's a simple implementation of the 4th order Runge-Kutta method in C++:

#include <iostream>
using namespace std;

double f(double t, double y) {
    return t * y; // Example function dy/dt = t * y
}

void rungeKutta(double t0, double y0, double t, double h) {
    int n = (int)((t - t0) / h);
    double k1, k2, k3, k4;
    double y = y0;

    for (int i = 0; i < n; i++) {
        k1 = h * f(t0, y);
        k2 = h * f(t0 + h / 2, y + k1 / 2);
        k3 = h * f(t0 + h / 2, y + k2 / 2);
        k4 = h * f(t0 + h, y + k3);
        y += (k1 + 2 * k2 + 2 * k3 + k4) / 6;
        t0 += h;
    }
    cout << "Approximate solution at t = " << t << " is y = " << y << endl;
}

int main() {
    rungeKutta(0, 1, 2, 0.1);
    return 0;
}

This will give you an approximate solution for the ODE.