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Questions on the numerical functions of Mathematica, implementing numerical methods and numerical computing with Mathematica.

5
votes
This function returns the location of the first place at which the decimal representations of the given numbers differ. firstDecimalPlaceDifference[x__] := If[Equal @@ SetPrecision[{x}, Infinity], …
answered Mar 9 '15 by 2012rcampion
12
votes
It seems I found my answer in OleksandrR's comment to this question. He says, Bear in mind Equal applies an extra tolerance in Mathematica. The proper comparison is Block[{Internal`$EqualToleran …
answered Mar 10 '15 by 2012rcampion
7
votes
Instead of doing the integration yourself, why not have Mathematica do it for you? g = 6.674*^-11; dt = 0.001; tStop = 2000; soln = First@NDSolve[{ x1''[t] == g (m2/Norm[x2[t] - x1[t]]^3 ( …
answered Apr 26 '15 by 2012rcampion
23
votes
2answers
Let's define two different numbers. x = 1. y = 1. + 2^-52 (* equivalently, 1 + $MachineEpsilon *) Let's make sure they're different with FullForm: x // FullForm (* 1.` *) y // FullForm (* 1.000000 …
asked Mar 9 '15 by 2012rcampion
3
votes
If you can tolerate some slowdown, use arbitrary-precision numbers instead of machine-precision numbers. Unlike machine-precision numbers, arbitrary-precision numbers keep track of how error propagat …
answered Jan 29 '15 by 2012rcampion