Any given a numerical method can be said to be stable or non-stable.
Let denote the growth of the error after subsequent operations, and denote the error in any given step of the calculations.
- If , we say that the error growth is linear ( being a constant that’s independent from )
- We call a method with a linear error growth a stable method
- If for a given , the growth of the error is exponential
- We call a method with an exponential error growth an unstable method
Things to Consider
Most of the time, a linear error growth is inevitable. When and are small, the results of the method are generally acceptable.
An exponential error growth should be avoided, since will be big even for small values of . This results in unacceptable inaccuracies.