If a problem is well-posed, then it stands a good chance of solution on a computer using a stable algorithm. If it's not well-posed, it needs to be re-formulated for numerical treatment.

The concept of well-posedness is related to that of continuity. In fact, if the problem can be thought of as a function mapping its data, which is an -tuple of real numbers, into its solution, an -tuple of real numbers, then well-posedness of the problem is the continuity of the function.

See also Numerical analysis, condition number