I was reading a paper and came up with this statement.
Stability merely avoids uncontrolled error growth but cannot guarantee actual numerical accuracy.
From what I understood from the concept of order of accuracy, the order of accuracy is the rate of convergence of a numerical approximation of a differential equation to the exact solution.
The larger the error, the more the numerical approximation won't converge to the exact solution. Am I correct?
But why a stable method where the error is controlled cannot guarantee numerical accuracy?
Could somebody please clarify a bit about this concept?