What are the differences between Euler and Runge-Kutta methods in numerical analysis and which method is more accurate for solving differential equations?

The main difference between Euler and Runge-Kutta methods in numerical analysis is the way they approximate the solution of differential equations. Euler method is a simple and straightforward approach that uses a first-order approximation, while Runge-Kutta method is more complex and uses higher-order approximations to improve accuracy. In general, Runge-Kutta method is more accurate than Euler method for solving differential equations, especially for complex or stiff systems.