I have code that is essentially numerical. It uses functions like NDSolve
and NIntegrate
. But in most interesting cases, the numerics are quite delicate and requires increasing the WorkingPrecision
and PrecisionGoal
.
Most of the numbers appearing in the equations in NIntegrate
and NDSolve
are given in decimal form: like eps = 0.0001
and xMax = 20.5
. Mathematica treats these as MachinePrecision
numbers. This causes error messages by NDSolve
and NIntegrate
when WorkingPrecision
is increased:
"The precision of the equations/integrand is less than the working precision"
So if I want these numerical functions to accommodate any value for WorkingPrecision
, it seems I have to express these numbers like eps = 1/10000
and xMax = 205/10
or eps=0.0001`100000000000
and xMax = 20.5`10000000000
. These options make for unreadable code.
For the sake of readable code, how do I tell Mathematica that all numbers are to be treated as arbitrary precision numbers?