What are the different numerical methods and how do they compare?

What are the different numerical methods used in mathematics?

Numerical methods include techniques like the Newton-Raphson method, Euler's method, and the Runge-Kutta method, among others.

How do these methods compare in terms of accuracy and efficiency?

Generally, methods like the Runge-Kutta are more accurate but computationally intensive, while Euler's method is simpler but less accurate.

Can you give me an example of when to use each method?

Sure! Use Euler's method for simple problems where speed is essential, and the Runge-Kutta method for more complex problems requiring higher accuracy.

What are the limitations of these numerical methods?

Limitations include issues like convergence, stability, and the potential for significant errors in certain conditions.