Getting the result to be deterministic is only the start of the problem. How do you know it is _correct_, or more properly, know the error bounds involved? How much does it matter to your problem?
e.g. If I am doing a 48-hour weather forecast, I can compare my results with observations next week; I can treat numerical error as a part of "model" error along with input observational uncertainty, etc.
I might validate part of my solutions by checking that, for example, the total water content of my planet doesn't change. For a 48-hour forecast, I might tolerate methods that slightly lose water over 48 hours in return for a fast solution. For a climate forecast/projection, this would be unacceptable.
Getting the same answer every time is no comfort if I have no way of knowing if its the right answer.