Numerical methods for ODEs - Truncation error and the order

In this video we are going to look at some error analysis for 1st order ODEs and look at the order of the method in relation to the local truncation error.

[@timshelton9278]

Clear message, clear structure, easy to understand, thank you

[@cameronspalding9792]

The way the truncation error is defined can vary depending on the author

[@gangigooga7710]

What is theta representing?

[@cameronspalding9792]

Gangigooga it represents a value that satisfies the equation: if you look at Lagrange’s reminder theorem the remainder takes the form h^2/2* second derivative evualuated at theta for some suitable theta

[@blakeholowaty4462]

what does it even mean to say "the order of error" ? Like I know its of the form "O(h^p)" , but what does that even mean? Anything would be much appreciated.

[@sashacurcic1719]

It refers to the order of the first Taylor Expansion term which isn't accounted for by the numerical approximation.

[@angshumanbhardwaj5664]

it means how quickly the error drops as h is reduced. so order h error drops linearly with h, order h^2 drops quadratically with h and so on.

[@username9951]

What is haych? ;)

[@erick2051]

I almost dont get what he was saying hahah