Hello Eric,

Thanks again for your comments and suggestions, I really appreciate all the time you have spent looking at my examples. I need to take time to experiment with the ideas shared but I will post a response to let you know if I overcome my current issues.

Hans - thank for the tip on editing the overall thread title.

Bye, David

Just started looking, but I've already seen something I want to comment on. Integers and rationals are generally handled as perfect/infinite precision quantities by Mathematica. So, for example, optEXP = 20`50; is actually less precise than just optEXP = 20;. If you want high precision, one strategy is to stick with infinite precision as long as possible, but here you've already "corrupted" any calculations using optEXP. [Note, obviously you may need to trade speed for precision.]

So, this:

sK = 2.46227`50;
sA = 53.401191`50;
optC = 200.0`50;
optEXP = 20`50;
wK = optC/sA^2;

could be this instead:

sK = Rationalize[2.46227`50];
sA = Rationalize[53.401191`50];
optC = 200;
optEXP = 20;
wK = optC/sA^2;

And this:

voverE[r_] := (4`30/sK)*(1`50/r^12 - 1`50/r^6) - (I*wK)*(1`50/r)^optEXP

could be this:

voverE[r_] := (4/sK)*(1/r^12 - 1/r^6) - (I*wK)*(1/r)^optEXP

We could better help you if you provided some sample code that represents what you want to do. In the meantime, I'll guess that you are running into a common challenge for new Mathematica users trying to control precision. Whenever you write a number like 1.0, i.e. anytime you use a decimal point and no other precision info, you are specifying a number with machine precision (about 16 decimal digits). Once you've committed to a particular precision, you cannot expect precision to increase in subsequent calculations. Setting the working precision for a particular calculation cannot increase the precision of the quantities you feed to that calculation. So, the general strategies are to use infinite precision quantities for your inputs (things like integers or Pi) or to specify the precision of your inputs sufficiently high. One way to specify precision is with a backtick, e.g. 1.0`100 (approximately 100 digits of precision in this case). But again, we'd need a concrete example of what you're trying to do to provide more specific guidance.

Have you read the documentation for FindRoot? There are examples of how to use AccuracyGoal, PrecisionGoal, and WorkingPrecision. I am able to get results to very high precision by tweaking those options. Please don't provide a complicated notebook. Just provide a single, simple, representative example of something that doesn't give you what you expect.

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