I need to solve an ODE with very high precision. I am not sure yet how much precision I need so I have some question before changing the settings.
From what I understand, the working precision is how many digits the machine uses for calculation. Is this decimal digits? Can I specify binary digits? Will I gain anything by specifying binary digits?
What is the difference between AccuracyGoal and PrecisionGoal? Their description is the same. Assuming that I want 50 correct digits, which one should I set and what working precision should I choose? Is there a rule of thumb I should follow?
How certain can I be about the precision of the result? Is there any way to keep track of the error?
Can I compile with arbitrary precision? If yes, what type do I declare? Is there any other trick that I can use to speed things up?