C++ Numerical Methods

What are numerical methods in C++?

Numerical methods in C++ are algorithms used to solve mathematical problems numerically, such as integration and differential equations.

Can you give me an example of a numerical method implemented in C++?

Sure! One common example is the Newton-Raphson method for finding roots of equations. Would you like to see the code?

Yes, please show me the code for the Newton-Raphson method.

Here's a simple implementation:

#include <iostream>
#include <cmath>

double f(double x) {
    return x*x - 2; // Example function: x^2 - 2
}

double f_prime(double x) {
    return 2*x; // Derivative of the function
}

double newtonRaphson(double initialGuess, double tolerance) {
    double x = initialGuess;
    while (fabs(f(x)) > tolerance) {
        x = x - f(x) / f_prime(x);
    }
    return x;
}

int main() {
    double root = newtonRaphson(1.0, 0.0001);
    std::cout << "Root: " << root << std::endl;
    return 0;
}

This code finds the square root of 2.

What are some other numerical methods I can learn about?

You can explore methods like the Euler method for solving ODEs, the Runge-Kutta methods, and numerical integration techniques like Simpson's rule.