Discretization error

Discretization error is about making things simpler so we can understand them better. Think of a drawing of a cat. If someone drew a perfect cat, it would be amazing. But most of the time, drawings are made up of lines and curves that approximate the shape and style of a cat. This is similar to what happens when we use computers to solve problems.

When people use computers to solve problems, they turn them into a bunch of numbers and equations. We say that they "discretize" the problem. This is like making a drawing of a cat with a bunch of dots and lines. It's not as good as a real cat, but it's easier to work with.

But there's a problem with discretization. Just like a drawing of a cat isn't a real cat, the numbers and equations that computers use aren't exactly the same as the real problem. This means that there will be some "discretization error." It's like if you drew a cat and it looked a little bit weird because you didn't quite get the shapes right.

This error can be really small, and sometimes it doesn't matter. But sometimes it can be really big and cause problems. That's why when people use computers to solve problems, they have to be careful to make sure that the discretization error is as small as possible.