truncation error

The above definitions are particularly relevant in situations where truncation errors are not important.

We therefore have a truncation error of 0.01.

Additionally, truncation error can also become an issue.

The local truncation error of the Euler method is error made in a single step.

An expression of general interest is the local truncation error of a method.

This means that, in this case, the local truncation error is proportional to the step size.

The total truncation error, considering both sources, is upper bounded by:

These can be derived from the definition of the truncation error itself.

The definition of the global truncation error is also unchanged.

The relation between local and global truncation errors is slightly different than in the simpler setting of one-step methods.