Numerical methods are really important for solving tricky math problems called differential equations. Sometimes, finding an exact answer is too hard or even impossible, so we use these methods instead.

Let’s break it down:

1. Accuracy: There are different ways to use numerical methods, like Euler's method and Runge-Kutta. These methods can give us answers that are very close to the correct ones, with only a small error. The error can be about $O(h^2)$ to $O(h^4)$, depending on which method we choose.

2. Applications: Research shows that more than 70% of real-life problems, especially in fields like physics and engineering, use numerical methods to find solutions to differential equations. That’s a lot!

3. Computational Efficiency: Thanks to the latest technology, we can use these methods to work with systems that have thousands of equations. This shows how our computers make it easier to solve complex problems more quickly and effectively.

In simple terms, numerical methods help us tackle math challenges that would otherwise be too tough to handle!