Numerical methods for ordinary differential equations

Numerical methods for ordinary differential equations (ODEs) are ways of using math to solve ODEs. ODEs are equations that describe how something changes over time, like how the position of a car changes as it drives down the road.

Numerical methods use simple math operations, like addition, subtraction, and multiplication, to break the ODE down into small steps that can be used to approximate the answer. To do this, the equation is split into many sections that are small enough that the equation looks like it's not changing much. This is a bit like slicing an apple into many thin slices so it looks like a whole apple.

To solve these small pieces, a computer is used to keep track of all the numbers and apply the math operations over and over again. Each time it combines the results of all the operations, it gets closer and closer to the answer.

When the computer finishes solving the small steps, all the results are put back together to get an approximation of the answer to the ODE. This is how numerical methods are used to solve ODEs and get an answer without actually solving the equation completely.