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For a long time I have been searching for an answer to the link or the relation between AccuracyGoal, PrecisionGoal, and WorkingPrecision. I want to use them in NDSolve.

I read most of the answers on this website and other websites but I didn't get any useful answers. All I got is that WorkingPrecision should be higher than AccuracyGoal and PrecisionGoal.

Can someone please explain the relationship between them not in a detailed numerical way? And how can I know which value is appropriate to my initial values?

Note: I edited my question since it seemed like: Is manual adjustment of AccuracyGoal and PrecisionGoal useless? . I checked it and its answers before I asked. Its answers are in detail and explain the usage and the meaning of those options. But they didn't hit my point, since in my work I'm not going deep into the numerical issues.

All that I want is:

1- How I should choose the value of AccuracyGoal depending on my inputs?

2- What is the relation between AccuracyGoal, PrecisionGoal, and WorkingPrecision? (Here I mean if I set AccuracyGoal -> k what should the value of PrecisionGoal and WorkingPrecision be?)

Maybe I got an answer to my second question from the answers on this website (If AccuracyGoal -> k then PrecisionGoal -> k and WorkingPrecision -> 2k). Is this correct?

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    $\begingroup$ > "How I should choose the value of AccuracyGoal depending on my inputs?" What inputs, for what problem? Choose AccuracyGoal - > k if it is acceptable that solution errors less than $10^{-k}$ may be treated as equivalent to zero. This is stated in an answer to one or both of the duplicates. $\endgroup$
    – Michael E2
    Commented Oct 27 at 2:21
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    $\begingroup$ Typically, if one sets WorkingPrecision -> 2k, then AccuracyGoal and PrecisionGoal are automatically set to k. This is a heuristic. Whether it works depends on the problem, which you have not given. The dependency of each of the three option values depends on the problem, which you have not given. But this dependency is explained in the linked Q&As. $\endgroup$
    – Michael E2
    Commented Oct 27 at 2:35

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